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Development of designmethods for lamella
separators
This item was submitted to Loughborough University's Institutional Repositoryby the/an author.
Additional Information:
• See also: Deborah J. BROWN. `Design of lamella separators. Part 2.'(Ph.D. thesis, Loughborough University.) Loughborough : LoughboroughUniversity, 1986.
• A Doctoral Thesis. Submitted in partial fulfilment of the requirementsfor the award of Doctor of Philosophy at Loughborough University.
Metadata Record: https://dspace.lboro.ac.uk/2134/27215
Publisher: c© P.H. Poh
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LOUGHBOROUGH UNIVERSITY OF TECHNOLOGY
LIBRARY
AUTHORIFILlNG TITLE
____________ e~_I:!+_ J'_t! ____ ---------------~ ---------------------------------- --- ----- - --_._------
ACCESSIONICOPY NO.
________________ 9 ~_~ ~_'T_~/~_~ __________ --------VOL. NO. CLASS MARK
-3. ,!IP ';187 18 MAY 2008 30 JUN 1995
1 3 NOV 1992
Jg1 f.W",!J9jJJ 1. ~~~ \~~~ - NOV 1996
- t JUt 1994 -~7 - 1 JUl1994 '
DEVELOPMENT OF DESIGN METHODS FOR LAMELLA SEPARATORS
Supervisor:
by
P.H. POH BSc, DIS·
Submitted for the Degree of
Doctor of phil osophy
of Loughborough University of Technology
April 1984
Department of Chemical Engineering
Director of Research: A.S. Ward BScTech, CEng,
MIChemE, AMCST Professor D.C.Freshwater BSc,
PhD, DLC (Sci), CEng, FIChemE Dean of Pure and Applied Science Loughborough University of
Techno 1 ogy
o by P .H. POH, 1984
1 ~h~ .. rt'~sh Unl~..mty 0' T-echra~)t:'1i-· l. r~lnry
fiM~ " n'-~ Clan
.-.. D Cl s: 3 \!-I) Je"1.-Ne. ,
In research the horizon reaedes as we
advanae. and is no nearer at sixty than
it was at twenty. As the power of
enduranae weakens with age. the urgenay
Of the pursuit grows more intense ••• and researah is aZways inaompZete.
Isaac Casaubon (1875)
ABSTRACT
Some guidelines for the design of a parallel plate lamella
separator have been derived from an improved understanding of
the various aspects of inclined sedimentation. These include . the adequate'provision of the essential requirements for achie
ving laminar and steady-state conditions. flow stability and an
efficient sludge discharge along the lower inclined surfaces.
A novel laser-photographic technique has been used to assist in
these studies.
Two possible optimum operating conditions have been esta
blished which highlight the potential for upgrading the efficiency
of eXisting lamella separator design. The first is an optimum
inclination angle at which the desired level of sludge thickening
is achievable at the maximum separator throughput. The second is
an optimum channel length to channel spacing ratio for the separa
tor to minimise the adverse effect of particle re-entrainment
induced mainly by flow instabil'ity. This will ensure the most
economic use of the lamella plates. Present findings suggest that
in the existing design the l~tter may be overdesigned by a factor
of 2 or even greater.
It is shown that the Nakamura and Kuroda equation is indeed
capable of adequately predicting the separating capabilities of
both batch and continuous separators. The tested range of condi
tions over which the equation is applicable are:
i
Ro ~ 0(1) - 0(10)
In the absence of any significant flow instability, near perfect
agreement is obtained between the predicted and the actual maximum
overflow rates for t~e contin~ous separator. This compares very , .
favourably with the 50 percent agreement currently reported 1n
the literature.
A more· comprehensive design scheme is proposed in which
constraints are imposed on the relevant design variables in order
tosuppress the various potential causes of non-idealities. Examples
of the latter include poor sludge flow and particle re-entrainment.
By taking steps to avert the creation of these non-ideal conditions,
it is believed that substantial improvement to the overall design
can be achieved.
Finally, it is ratified that the cocurrent supercritical mode
is a more superior method of operating a lamella separator. Its
two main advantages are:
i) it is a relatively more stable system and hence reduces the
problems of particle re-entrainment;
ii) it shows a greater potential to achieve high quality sludge
thickening performances.
,
i i
ACKNOWLEDGEMENTS
The author is indebted for the invaluable guidance and
encouragement of Mr Anthony S. Ward (Project Supervisor) during
the course of this work.
The financial support of the Science and Engineering
Research Council is gratefully acknowledged.
Finally, the author wishes to express his gratitude to the
following individuals:
Professor D.C. Freshwater for providing the research facilities.
Members of staff of the Particle Technology Group of the Chemical
Engineering Department for their encouragement and useful
discussions.
Mr G. Boyden for photographic services.
Mr I. Sinclair for advice on Laser Doppler Anemometry.
Mr R. McTernan for his assistance in operating the continuous rig.
Mrs J. Smith for typing the thesis.
My family for their enormous support and source of inspiration •
...
iii
Abstract ...
CONTENTS (A detailed contents list is given at the beginning of each chapt~r)
Acknowledgements
Contents , ...
List of Tables
List of Figures
CHAPTER 1: INTRODUCTION
CHAPTER 2: LITERATURE REVIEW
Page No
i
iii
iv
· .. v
vii
1
5
CHAPTER 3: EXISTING DESIGN METHODS FORLA~lELLA SEPARATORS 47
CHAPTER 4:
CHAPTER 5:
CHAPTER 6:
CHAPTER 7:
CHAPTER 8:
Appendices
Nome nc 1 a ture
DEVELOPMENT OF DESIGN METHODS
EXPERIMENTAL PROGRAMME
DISCUSSION OF RESULTS
CONCLUSIONS
RECOMMENDATIONS FOR FURTHER WORK
Bibliography ••• ...
iv
58
93
· .. 127
198
202
204
282
· . • 286
TabZe No.
2.1
2.2
4.1
5.1
5.2
6.1
6.2
6.3
6.4
6.5
6.6
6.7
LIST OF TABLES
Desaription
Factors influencing the choice of flow pattern ... Surface loadings on typical applications (lamella separators)
Summary of design variables and constraints
Closely matched refractive index system
The different fully dispersed systems used in the sludge flow experiments
Experimental verification of the position of discontinuity: high aspect ratio case
Experimental verification of the predicted rate of batch inclined sedimentation using the Nakamura and Kuroda equation: low aspect ratio case •.•
Sludge flow behaviour of the different fully dispersed systems ••• • ••
Effect of size of solids on the layer movement •••
Effect of solids density on the required angle of inclination for layer movement
Effect of liquid viscosity ~n layer movement .•.
Accuracy of the Nakamura-Kuroda equation in predicting the maximum overflow rate (Q ) at Co = 0.5% v/v for the different moHes of operation - b = 3.4 cm ...
v
Page No.
30
44
89
98
121
138
144
151
153
155
157
163
TabLe No.
6.8
6.9
6.10
Desapiption
Accuracy of the Nakamura-Kuroda equation in predicting the maximum overflow rate (Qa) at Co = 2% v/v for the different moaes of operation - b = 3.4 cm '"
Accuracy of the Nakamura-Kuroda equation in predicting the maximum overflow rate (Qo) for countercurrent flow-with channel spacings of 1.5 cm and 3.4 cm at Co = 0.5% v/v •..
Accuracy of the Nakamura-Kuroda equation in predicting the maximum overflow rate (Qo) for countercurrent flow with channel spacings of 1.5 cm and 3.4 cm at Co = 2% v/v
vi
Page No.
169
171
172
FigUI'e No.
2.1
2.2
2.3
2.4
2.5
2.6
2.7 .
2.8
2.9
2.10
2.11
2.12
3.1
3.2
4.1
LIST OF FIGURES
Description
Boycott's observations ... Nakamura and Kuroda inclined sedimen-tation model ..• •
Oliver and Jenson inclined sedimentation model ..•
Three layer model by Probstein. Yung and Hicks
The subcritical and supercritical modes of operation '"
The different flow patterns for lamella separators
Dual flow clarifier -.... Clarifier-thickener unit
Typical design arrangement for achie-ving even flow distribution '"
Commercial countercurrent flow lamella plate separator by Parkson Corp.
Effect of low amplitude vibration on the compression of sludge
Chevron-design settling channel
Limiting trajectory for settling par-ticle .. ~ ...
Steady-state conditions proposed by Jernqvist
Coordinate system showing the variables used in the analysis of flow motion in a low aspect ratio vessel (parallel plate)
vii
Page No.
8
11
14
20
21
27
28
28
32
35
36
38
54
56
67
Figu:r'e No. Description Page No.
4.2 Batch settling behaviour in a high aspect ratio separator 73
4.3 Typical velocity profile for the countercurrent and cocurrent-sub-critical modes of operation 79
4.4 Typical velocity profile for the -- cocurrent-supercri tica 1 mode of
80 operation
4.5 Proposed design scheme for lamella separators 92
5.1 Experimental arrangement for laser-photographic analysis ••. 102
5.2 Arrangement of Ha lvern Laser Anemometer operating in the forward scatter mode 105
5.3(a) Signal processor of Laser Anemometer (b) Experimental arrangement for liquid
106 velocity measurements ... · .. 5.4 Typical oscilloscope trace from Laser
Doppler Anemometer · .. 109
5.5 Typical oscilloscope trace from present experiments showing negligible turbu-lence III
5.6 Agitator for batch settler 112
5.7 Experimental rig for continuous lamella separator 116
5.8 Continuous flow arrangement 118
5.9 Hicrographs of solids used in the diff-erent fully dispersed systems · .. 122
5.10 Experimental rig for the study of sludge flow behaviour ..• 124
vi i i
FiguPe No. Description Page No.
6.1 Comparison between the theoretical and measured thicknesses of the clear liquid layer along the upper inclined surface of a parallel sided batch separator: (h/v) = 1.13; 6 = 600 and Co = 1-30% v/v 130
6.2 Comparison between the theoretical and measured thicknesses of the clear liquid layer along the upper inclined surface of a parallel sided batch separator: (h/b) = 3.42; 6 = 200 and Co = 1-30% v/v 131
6.3 Comparison between the theoretical and measured thicknesses of the clear liquid layer along the upper inclined surface of a parallel sided batch separator: (h/b) = 3.42; 6 = 300 and Co = 1-30% v/v 132
6.4 Comparison between the predicted and measured longi tudina l·components· of.···.,·· .•.. eT ..
liquid velocity in the clear liquid layer for a parallel sided batch separator:
135 (h/b) = 1.8; e = 450 ; Co = 1-2~% v/v
6.5 Comparison between the predicted and measured longitudinal components of liquid velocity in the clear liquid layer for a parallel sided batch separator: (h/b) = 3.78; 6 = 200 and Co = l-2~% v/v 136
6.6 Comparison between the theoretical and measured thicknesses of the clear liquid layer along the upper inclined surface for a parallel sided batch separator: (h/b) = 41.31; 6 = 700 and Co = 1-5% v/v 140
6.7 Comparison between the theoretical and measured thicknesses of the clear liquid layer along the upper inclined surface for a parallel sided batch separator: (h/b) = 64; 6 = 450 and Co = 5-15% v/v 141
6.8 Comparison between the theoretical and measured thicknesses of the clear liquid layer along the upper inclined surface for a parallel sided batch separator: (h/b) = 75; 6 = 300 and Co = 2~% v/v 142
ix
FiguPe No. Description Page No.
6.9 The different mechanisms of sludge flow a) Bulk movement. b) Heap movement. and c) Layer movement 149
6.10 Effect of shape and surface ~exture of sl udge soli ds on the 1 ay er movement 159
6.11(a) Re-entrainment of particles into the clear liquid layer due to unfavourable velocity profile (countercurrent flow) 166
6.11(b) Re-entrainment of particles due to the combined effects of an unfavourable velocity profile and interfacial instability (countercurrent flow) 166
6.12(a) Formation of "interfacial wave" due to flow instability (cocurrent-supercritica1 mode) 167
6.12(b) Re-entrainment of particles into the clear liquid layer due to wave breakages brought about by flow instability (cocurrent-supercritica1 mode) 167
6.13 Effect of separator aspect ratio on the actual maximum overflow rate for the countercurrent flow with c = 0.5% v/v .. b = 3.4 cm and e = 200-6000 (from the vertical) 176
6.14 Effect of separator aspect ratio on the actual maximum overflow rate for the cocurrent-subcritica1 mode with Co = 0.5% v/v. b = 3.4 cm and e = 200 -600 177
6.15 Effect of separator aspect ratio on the actual maximum overflow rate for the cocurrent-supercritica1 mode with Co = 0.5% v/v. b = 3.4 cm and e = 200 -600 178
6.16 Effect of separator aspect ratio on the actual maximum overflow rate for the countercurrent flow with Co = 2% v/v. b = 3.4 cm and e = 200 -600 • 179
x
Figure No.
6.17
6.18
6.19
6.20
6.21
6.22
6.23
6.24
Description
Effect of separator aspect ratio on the actual maximum overflow rate for the cocurrent-subcritical mode with Co = 2% v/v. b = 3.4 cm and e = 200-600
Effect of separator aspect ratio on the actual maximum overflow rate 'for the cocurrent-supercritical mode with Co = 2% v/v. b = 3.4 cm and e = 200 -600
Effect of inclination angle on the consistency of the solids concentration (c ) in the underflow stream for the counter!! current flow with the initial feed concentration at 0.5% v/v
Effect of inclination angle on the consistency of the solids concentration in the underflow stream for the cocurrent-subcritical mode with the .. initial. feed. concentration at 0.5% v/v
Effect of inclination angle on the consistency of the solids concentration in the underflow stream for the cocurrent-supercritical mode with the initial feed concentration at 0.5% v/v ••.
Effect of inclination angle on the average "steady-state" solids concentration in the underflow stream for the different flow patterns at Co = 0.5% v/v
Effect of inclination angle on the consistency of the solids concentration in the underflow stream for the countercurrent flow with the initial feed ·concentration at 2% v/v
Effect of inclination angle on the consistency of the solids concentration in the underflow stream for the cocurrent-subcritical mode with the initial feed concentra ti on at 2% v/v
xi
Page No.
-- 180
181
185
186
187
188
193
194
Figure No. Description Page No.
6.25 Effect of inclination angle on the consistency of the solids concentration in the underflow stream for the cocurrentsupercritical mode with the initial feed concentration at 2% v/v... 195
, 6.26 Effect of inclination angle on the average
"steady-state" solids concentration in the underflow stream for the different flow patterns at Co = 2% v/v... 196
xii
CHAPTER 1
INTRODUCTION
The separation of solid particles from liquid streams is an
important step to a wide range of industrial applications. The .
simplest and most common method of achieving this is by means of . gravity sedimentation which, however, often requires large tanks
with extensive settling areas: especially when the particles in
the suspension are small and slow settling •. Thus there exists a
need to design high-rate settlers which have shorter detention
times, i.e. of the order of minutes rather than hours.
In recent years, the approach taken has been one of incor
porating extended inclined surfaces-in a conventional settler to
enhance the settling rate and by increasing the total projected
area available for sedimentation. Such a settler is commonly
referred to as a lamella separator. Compared with the conven
tional settlers, the users of lamella separators can expect to
have the benefits of lower capital and operating costs, and the
potential of higher separating efficiencies.
Hitherto, applied research on the behaviour of suspensions
settling under the influence of inclined surfaces is limited in
its extent and in its accuracy. Almost all the models previously
developed are either oversimplistic or contain too many ad-hoc
assumptions and therefore cannot establish the limitations within
which they are applicable. Consequently, process engineers speci
fying this type of equipment do nothave reliable design methods
1
and tend to rely heavily on empirical findings and past industrial
experience to substantiate the final design specifications. 'This
situation is often undesirable because it demands extensive pilot
plant experiments which are both time consuming and costly. The
more well tested design methods that have been reported in the
1 iterature invol ve either imposing an "improvement factor" on the
Goe and GleVe~ger13 procedure for conventional thickeners,or adding
another term to the renowned Yoshi oka 68 procedure. The "improve
ment factor" is based on the Nakamura and Kuroda42 formula deve-
loped to predict the enhanced rate of sedimentation in an inclined
vessel. However, the proponents of these design methods concede
that their procedures are only about 50% accurate. A detailed
review of the 1 iterature on the theory of incl ined sedimentati on
and the existing design methods for lamella separators is given
in Ghapte rs 2 and 3.
This research work aims to rectify the deficiencies highlighted
above through the following objectives:
i) to improve the understanding of the inclined sedimentation
process, and hence provide a basis for developing the means
of predicting and interpreting the overall settling behaviour
in a continuous system;
ii) to establish optimum operating conditions;
i i i) to estab 1 is.h a useful si zing method that not only predi cts
the area requirements but also provides the conditions
under which it is applicable, and
2
iv) to develop a more comprehensive design scheme for lamella
separators, i.e. one that incorporates all the relevant
design elements and constraints, as listed below:
Steaqy-state constraint
Laminar flow constraint
)
~ to enable the formation of steady
state stratified viscous layers in
the settling channel (i.e. the
clear liquid layer, the suspension
layer and the sludge layer).
Flow stability constraint: to minimise the re-entrainment of
particles from the suspension
layer into the clear liquid layer.
Sludge flow constraint:' .'. to ensure a: continual and rapid-"
removal of sludge formed on the
lower inclined surfaces.
The research programme that is designed to achieve these objectives
is fully described in Chapter 4.
Chapter 5 covers the experimental programme that is devised
principally to verify the theoretical predictions of inclined
sedimentation behaviour in both batch and continuous systems.
However, also included in the programme are exploratory experi
ments to study, in particular, the mechanisms and parameters
governing the sludge flow behaviour on the lower- inclined surfaces.
It is found from existing literature that this area of research
has been severely neglected and no theoretical attempt to model the
sludge flow behaviour has ever been made.
3
Also contained in this chapter are details of the experi
mental facilities. i.e.
details of the experimental rigs
- details of the experimental techniques and operating
- procedures. and
- materials used in the experiments and their selection
cri teria.
All the experimental results are analysed and discussed in
Chapter 6.
Finally. in Chapter 7 the conclusions from this research
work are presented; and recommendations are made for further work
in Chapter 8.
4
2.1 THEORY 2.1.1 2.1.2 2.1. 3
2.1.4
CHAPTER 2
LITERATURE REVIEW
Batch inclined sedimentation models Continuous inclined sedimentation models Inclined settling behaviour 'of floccula-ted suspensions '" Inclined settling behaviour of non-flocculated suspension '"
·2.2 PRACTICAL DESIGN CONSIDERATIONS · .. 2.2.1
2.2.2
Flow patterns · .. 2.2.1.1 Types of flow pattern 2.2.1.2 Factors influencing the choice
of flow pattern '" Hydraulic conditions ••• 2.2.2;1 Laminar flow ••• • ••
2.2.2.2 Even flow distribution '" 2.2;2.3 Environmental factor: adverse
effect of temperature variation 2.2.3 Geometric parameters •.•
2.2.3.1 Plate spacing 2.2;3.2 Angle of inclination
· ..
'" 2.2.4 2.2.5 2.2.6 2.2.7 2.2.8
Feed entry ;;. Design.of sludge collector Design-of settling channels Pretreatment of suspensions Materials of construction
2.3 INDUSTRIAL APPLICATIONS Water treatment Waste water treatment Mining
· .. '"
'"
· .. ...
2.3.1 2.3.2
2.3.3 2.3.4 Surface loadings on typical applications
5
Page No 7
7
18
22
24
26 26 26
29 30
30
31
31 33
33
33 34 34 36
38 39
40
40
42 43 44
2.4 ADVANTAGES AND DISADVANTAGE~ OF LAMELLA SEPARATORS 2.4.1 Advantages... '"
2.4.1.1 Low capital and operating costs 2.4.1.2 Higher separating efficiency 2.4.1.3 Convenience of construction and
installation ••• '" 2.4.1.4 Fewer maintenance problems
2.4.2 Di sadvantages 2.4.2.1 Short sludge detention time for
compression ••• • •• 2.4.2.2 Susceptibility to fouling problems
6
Page No 45 45 45 45
45 46
46
46
46
2.1 THEORY
CHAPTER 2
LITERATURE REVIEW
It is well known that generally the separating capacity
of any sedimentation device is directly proportional to the
total horizontal area available. 10 ,22,SO Thus the most obvious
advantage of having extended surfaces within a sedimentation
device is in the provision of additional separating area.
Furthermore, by having the additional surfaces inclined extra
-beneficial effects can be achieved: for example, all the
particles that have settled on the lower inclined surfaces can
be made self-draining, and there is- a greater potential for
control of liquid flow pattern.
2.1.1 Batch inclined sedimentation models
Over the years some fair amount of research has been conduc
ted to describe (qualitatively and quantitatively) the phenomenon
of inclined sedimentation under different sets of conditions.
The first significant work was conducted by BoycottS, who studied
the sedimentation of blood corpuscles in test tubes. It was found
that-the sedimentation rate was increased when the tube was tilted
and that, for a given angle of tilt, sedimentation was faster in
tubes of smaller bore and in tubes in which the initial vertical
height of suspension was greater. These results are shown
diagrammatically in Figure 2.1. Boycott could not offer any
7
.'
(i) Effect of angle of tilt on settling rate
t 1
>,-,,- -.-- -'--.-. -----
(ii) Effect of initial height of suspension on settling rate
~--t:.:I_----%.t I
(iii) Effect of tube diameter on settling rate
FIGURE 2.1: BOYCOTT'S OBSERVATIONS
8
scientific explanation and interpreted this phenomenon as an
effect of Brownian movement of the lower corpuscles in the
settling column.
Subsequently many investigators, including Bercze11a and
Wast1 6, Linzenmeier35 and Lungren37 , advanced hypotheses to
explain Boycott's observations but all achieved limited success.
For example, Lungren proposed that an explanation for Boycott's
effect lay in the ability of liquid displaced by settling parti
cles to bypass percolation back up through the dense cloud of
falling particles by flowing upward beneath the upper inclined
surface. Though this idea could explain the effects of altering
the tube angle and bore, it could not explain the effect of
altering the initial vertical height of the suspension .. Clearly·
at this stage there was a desperate need for a fundamental model
to explain satisfactorily the behaviour of incline-sedimentation,
as \~e11 as to elucidate its commercial potential.
The earliest mathematical model to fu1fi11 some of those needs
was developed by Nakamura and Kuroda. Their model, which was
originally devised for sedimentation in an inclined square sec
tion tube set on its edge, depended on two vital assumptions:
i) only the downward facing surface accelerated sedimentation,
and
ii) the particles in the settling suspension tend to keep the
same distance apart until they aligned upon a solid surface
or upon other particles.
9
Details of the mathematical derivations are summarised as
follows. At the start of settling all particles on a surface
denoted by the line CAB (shown in Figure 2.2(a)) settle with an
initial velocity v for an elemental time dt and reach a hypo
thetical surface DFH. Because the velocity v is assumed to
have the same,value at all points, thus AF = BH = CD. The
volume of clear liquid displaced by the particles in time dt
is therefore represented by the shaded area ABGFEC (N.B. the
volumes represented by CDE and BGH are negligibly small and
may be neglected to simplify the mathematics). In reality,
however, the particles will not take up the surface shown as
EFG because of the density and height difference between the
suspension at plane FG arid the liquid at~pciint L' Aninsta:nta.:'
neous rearrangement will take place giving a new clear liquid
suspension interface at plane A'B' shown in Figure 2.2(b).
Nevertheless the two volumes of clear liquid shown must be equal
and thus the area AA'BB' must equal area ABGFEC. If the initial
height of the interface AB is h and this falls to a final value
(h-dh) after the elemen~il time dt, then, by equating the two
areas a mathematical relationship will be obtained relating the
enhanced rate of sedimentation to the suspension properties and
settler dimensions, i.e.
Eqn. 2.1
10
dt 1 1 A ,,....:uI.LUI.LU.J...1J..1..U.J...1J..1.I..I..LU-V-..!!---_~*_ h
(a) (b)
FIGURE 2.2: NAKAMURA AND KURODA INCLINED SEDIMENTATION MODEL
Similar derivations were made to describe the enhanced rate of
sedimentation in an inclined tube of circular section, i.e.
Eqn. 2.2
and for a square section tube resting on one corner, i.e.
Eqn. 2.3
Clearly from these equations it is evident that the tube confi-
guration and especially the square section tube resting on a
corner, should give higher set.tl ing r~tes than thesimple plane
lamella. This prediction has been verified by experimental
resul ts.
The Nakamura-Kuroda equations are apparently regarded to
represent an upper limit to the rate of sedimentation. Later
workers, including Graham and Lama19 and Vohra and Ghosh51,58,
found less enhancement of sedimentation. than predicted by the
equations and proposed the insertion of empirical coefficients
to account for the discrepancy. A further model requiring an
empirical constant has been proposed by Zahavi and Rubin69 •
Thi s model requi red both the constant determi ned for the enhan
ced sedimentation effect of the given fluid-particle system and
settling rate versus concentration data for vertical vessels.
The constant is taken to represent a fixed average rate of clear
fluid generation per unit area of the downward facing inclined
12
surface in the suspension. Agreement between the models and
experimental data was reported to range from good to fair.
The principal weakness of these models is that extensive
experiments are required to determine the empirical coeffi
cients, which are complex functions of the settler dimensions
and suspension properties.
Working with monodispersed polymer suspensions, 01iver
and Jenson29 ,44 observed that the clear liquid formed beneath
the upper inclined face of the tube was not as suggested by
Nakamura and Kuroda but in fact developed a roughly triangu1ar
shaped channel (shown in Figure 2.3). A mathematical model was
subsequently developed from the observed profile and the addi
tion of a simple convection term containing an empirical func
tion of concentration and angle of inclination. Mathematical
solutions describing the profile of the c1eari' liquid channel as
a function of time were obtained on an analog computer and the
general agreement with experiments was fair. However, the model
seemed to break down at high concentrations.
It is evident that all the models discussed so far are based
on only kinematic and geometric considerations. The fluid dynamic
aspects, which must have significant effects, have been virtually
ignored. Consequently, all these models suffer from at least two
serious limitations:
i) they cannot provide information about such flow characteris
tics as the state of motion and concentration distribution
within the suspension, and the clear liquid layer formation
which together affect the enhanced rate of sedimentation.
13
I) .
Clear liquid layer_----.,f::.
-.-''-i4--Susoension layer
FIGURE 2.3: OLIVER AND JENSON INCLINED SEDIMENTATION MODEL __ o·
ii) their range of validity is undefinab1e. Therefore any
mathematical equations derived from the models (e.g. Nakamura
and Kuroda), cannot be used for design purposes with any
degree of confidence, since it is impossible to tell under
what set of conditions (if any) they are expected to apply.
Attempts have recently been made by Hi11 23 ,24 and subsequently
by Acrivos and Herbo1zheimer2 to rectify the deficiencies highligh
ted above by developing more fundamental models based on the
applications of continuum mechanics. Hill established that the
enhancement of sedimentation in inclined channels results from
a naturally occurring settling convection32 which is caused
principally by particle momentum-transfer to the fluid. Based
14
on that mechanism of settling convection, a mathematical model
was subsequently developed to define the trajectories of
particles settling in very dilute suspensions. Using dimen
sional analysis, it was shown that aside from the geometric
factors such as the shape of the settler and the angle of
inclination, the settling process is in fact governed by two
dimension1ess parameters(*): NRe , a sedimentation Reyno1ds
number and NGR , a sedimentation Grashof number. The model
predicted that NRe should be made as small as possible and NGR
as large as possible to achieve the most rapid sedimentation.
Moreover, using experimental results and numerical solutions
from their mathematical model, Hill was able to establish a
rangeofva 1; dityf6r the Nakamura"and'l<Uroda"equations :" i:e:" ,
in the dual limit that NGR~ and NRe+O. In view of the limited
range and accuracy of their numerical solutions and experimental
data, that finding was then regarded as tentative.
Acrivos and Herbolzheimer2 have attempted to verify theo
retically the semi-empirical findings of Hill using analytical
techniques. Applying the principles of continuum mechanics, a
model is developed for describing quantitatively the sedimenta
tion of small particles in inclined channels. The model treats
the settling suspension as an effective fluid and assumes that
flow is 1aminar and the particle Reyno1ds number is small - both
assumptions are realistic for most industrial applications.
It is found that the enhanced rate of sedimentation is indeed
dependent on two parameters, in addition to the vessel geometry:
15
(*)
CI)
Definition and physical significance of dimensionless nuliibers
Sedimentation Grashof number (N GR) represents the signifi
cance of gravitational forces relative to viscous forces in
any convective flow. It is defined mathematically as:
h3g pep - p) Co N = P
GR 2 \l
(2.4)
(II) Sedimentation Reynolds number (NRe ) represents the signi
ficance of inertial forces to viscous forces in any convec-
tive flow. It is defined mathematically as:
NOTATION
h =
=
=
Pp =
P =
\l
g =
(2.5)
characteristic length of the macroscale motion
( .• which Hill took to be the initial height of
suspension)
initial volume fraction of particles
vertical settling velocity of the individual particles
at Co
density of the particles
density of the fluid
viscosity of the fluid
gravitational constant
16
a sedimentation Reynolds number which is typically small; and
A, the ratio of a sedimentation Grashof number to the Reynolds
number which is typically very large. By means of an asymptotic
analysis it is reaffirmed that, as A~ and for a given settler
geometry, the enhanced rate of sedimentation can be accurately
predicted with the use of Nakamura-Kuroda equations. The model
also produced an expression for the thickness of the clear liquid
layer formed beneath the downward facing surface as well as
velocity fields in the clear liquid and suspension layers. Under
the conditions of their experiments, excellent agreement was found
with theoretical predictions.
More recently Acrivos and Herbolzheimer3 extended their
previous analysis todescribethesedimentati6nof dilute SUSPEfn:'-"·
sions in narrow inclined channels, i.e. where their length in
relation to the channel spacing is large. (This is in contrast
with their earlier model where the length is of the same order
of magnitude as the channel spacing). Again, based on the
assumptions of laminar flow and small particle Reynolds number,
expressions were derived for the clear 1 iquid layer profile as
well as velocity fields in the clear liquid and suspension layers.
An unexpected outcome from the solution of the time-dependent
equations is that the clear liquid layer formed beneath the down
ward facing surface attains a steady-state profile only below a
critical point - above that point the thickness of the clear liquid
layer increases with time until it occupies the entire channel
spacing. The authors were able to show theoretically that because
17
of this transient behaviour the Nakamura and Kuroda equations
would overestimate the rate at which the top suspension/clear
liquid interface settled with time. However, the Nakamura and
Kuroda predictions for the owerall settling rate would still
hold under the conditions of the .model. Results of batch sedi-.
mentation experiments were found to be in excellent agreement
with the theoretical predictions. Another outcome of their
analysis, which is perhaps more important, is that the disconti
nuity in the clear liquid layer profile can be suppressed in
continuous settling systems but only if the feed and withdrawal
arrangements are properly designed with this aim.
2.1.2 Continuous inclined sedimentation models
Not only has little effort been directed to the development
of continuous inclined sedimentation models, but also most of the
existing ones are based on, or related to, an extension of the
well established continuous vertical sedimentation models
(i.e. the Yoshioka68 and Coe and Clevenger13 models). Mathematical
models developed by Zahavi and Rubin 70 , Graham and Lama 20 ,
Jernqvist30 and Obata and Watanabe43 are examples that fall into
this category. Agreement between theoretical predictions and
experimental data is generally fair.
Probstein, Yung and Hicks48,49 were the first to develop a
more fundamental dynamic flow model to describe the behaviour of
sedimentation in a continuous system. The model assumed that the
flow in any channel of the settler may be treated as comprising
18
of three viscous. stratified "fluid" layers. each of reasonably
uniform aensity moving under the action of gravity; a clarified
liquid. a feed suspension layer. and a sludge layer (see Figure
2.4). Two significant sets of results emerged from their model:
i) mathematical expressions of scaling laws which are useful
for design purposes. and
ii) that for a given settler throughput there exists two possible
operating modes (i.e. subcritical and supercritical). with
different velocity profiles. By definition. the subcritical
mode (shown in Figure 2.S(a)) is one in which the clear liquid
layer thickness is less than half the channel spacing at the
top of the· settl ing channel and decreasing gradually to a- -,.
minimum at the base of the channel. The supercritical mode
(shown in Figure 2.S(b)). on the other hand. is one where the
clear liquid layer thickness is greater than half at the top
and increasing gradually to a maximum at the base.
It is found that the latter mode is inherently more stable and
should serve as the basis for the design of a new type of lamella
settler with a higher throughput than present commercial settlers.
all of which operate in the subcritical mode. Both sets of results
have been verified experimentally.
In the recent work of Probstein and Leung33 the three layer
model above has been generalised and applied to evaluate the
performance of cocurrent flow lamella settlers and countercurrent
flow tube settlers. Their latest results seem to confirm the earlier
findings by Probstein. Yung and Hicks.
19
(1) Clear liquid layer (2) Suspension layer (3) Sl udge 1 ayer (A) Cocurrent flow (B) Countercurrent flow
FIGURE 2.4: THREE LAYER r·l0DEL OF PROBSTEIII, YUNG AND HICKS
20
Clear 1 iqui d
/ Feed
(a) Subcritical Mode
Clear liquid Feed
(b) Supercritical Mode
FIGURE 2.5: THE SUBCRITICAL AND SUPERCRITICAL MODES OF OPERATIm.
21
A more fundamental model by Acrivos and Herbolzheimer3
suggests that the ad-hoc assumptions made by Probstein and his
co-workers. regarding the existence of thr.ee steady-state strati
fied layers is oversimp1istic and hence only valid under certain
operating conditions. Their model showed •• for example. that in
cases where the feed is introduced into the settler along its
side. the feed and withdrawal locations must be chosen properly
to enable the formation of steady-state stratified layers.
Otherwise. transient behaviour will prevail. The subcritica1
and supercritica1 modes of operation have again been verified
theoreti ca 1ly.
2.1.3 Incline settling behaviour of floccu1ated suspensions
The batch settling behaviour of lightly f1occu1ated red mud
suspension in inclined tubes has been investigated experimentally
by Sarmiento and Uh1herr55 • It is postulated that there exists
three distinct settling regimes similar to those observed during
vertical settling of the san~ suspension: hindered settling.
channelling and compression. This is because the liquid-particle
and particle-particle mechanistic reactions are similar in nature.
even though incline settling is under the additional influence of
settling convection. The mechanisms of settling in each of the
regimes are summarised as follows:
22
i) Hindered settling of floes which maintain their size and
shape, and contain immobilised (intra-floc) liquid. At
this stage, only inter-floc liquid is displaced and flows
upwards between floes.
ii) Channelling: once contact of floes occurs they gradually
deform to produce a closer packing. This involves the expUl
sion of more inter-floc liquid mainly through stable channels
which are formed throughout the bed structure and may range
in diameter from several millimetres to micron size. Intra
floc liquid remains largely immobile.
iii) Compression: further subsidence causes compression and hence
decrease in the volume of floes with the elimination of intra
floc liquid both through channels initially and through the
floc structure finally.
Undoubtedly, all these mechanisms are operative simultaneously at
all times during the settling process. However, their relative
importance varies in the different regimes.
pearce46 ~/as one of the first researchers to study the
superimposed effects of settling convection on the sedimentation
of flocculated suspensions. His findingS suggest that two possible
responses can occur; if the original floes are strong, the circu
lating convection current "may encourage further flocculation to
create larger and faster settling floes. Conversely, if the floes
are weak to start with the convection current may break them down
to produce smaller and slower settling ones. It is obvious that
23
for practical purposes the latter case should be prevented from
occurring because of' two potential consequences. Firstly, the
overa 11 settl i ng effi ciency of the sus pens i on wi 11 drop because
of slower settling floes. Secondly, and for the same reason, the
probability of floes becoming re-entrained into the clear liquid
stream will increase dramatically.
From a design standpoint the results above highlight the
importance of flocculation as a pretreatment step to produce
strong and fast settling floes in order to optimise the actual
separation process. In addition, they provide a possible explana
tion for the deviations from theory (e.g. Nakamura-Kuroda) of the
actual settling rates of flocculated suspensions under inclined
surfaces. It is necessary to correct for the deviations in order
to fonmulate reliable predictive equations for design (sizing)
purposes.
2.1.4 Incline settling behaviour of non-flocculated suspensions
On a macroscopic scale the overall settling behaviour. of a non
flocculated suspension is similar to that observed in a flocculated
suspension. Both are influenced and characterised by the presence
of settling convection. However, on a microscopic scale the inter
particle and particle to liquid interactive forces are quite
different in nature as well as in magnitude. These differences
have given rise to a particular behaviour in non-flocculated sus
penions that distinguishes them from the flocculated ones: unlike
the latter, when the concentration has increased to the point where
24
the particles mechanically interact with one another, very little
further compression occurs. Any increase in concentration there
after arises due to the sliding and tumbling of particles over
one another until they reach a stable configuration. This is in
sharp contrast with the floc compression process that would have
occurred in a,flocculated suspension under the same condition.
In general, the treatment of non-flocculated suspensions is
expected to produce more compacted, higher bulk den'sity sludges
than flocculated suspensions which tend to be light and bulky.
25
2.2 PRACTICAL DESIGN CONSIDERATIONS
2.2.1 Flow patterns
2.2.1.1 Types of flow pattern
Continuous lamella separators commonly operate under 3 main
flow patterns:
i) Countercurrent flow (as illustrated in Figure 2.6(b» in which
the feed and sludge streams are in opposite directions,
ii) Cocurrent flow (as illustrated in Figure 2.6{b» in which
the feed and sludge streams are in the same direction, and
iii) Crosscurrent flow 39 ,52 (as illustrated in Figure 2.6{c» in
whi ch the di recti on of tllecfeed streamis perpendiculcar t~ Cc
the sludge stream. Of the three, the countercurrent flow
separator is much simpler in design and least expensive to
build.
Also available on the market are more complex deSigns such as the
dual flow clarification unit, as shown in Figure 2.7, where both
countercurrent flow and cocurrent flow can be achieved in the same
equipment. This is claimed by the manufacturer to have some
advantages where multiphase or heterogeneous systems are being
separated. Figure 2.8 shows a separator'unit in which clarification
and thickening may be achieved by having two packs of lamella
plates vertically above each other with the feed introduced
between them. The plate separations may be different in the two
packs and the lower pack may be vibrated, which can have beneficial
effects in the compaction of the sludge.
26
Clear liquid
Feed
(i) Countercurrent Flow
Clear liquid,,· Feed'
Sludge
(ii) Cocurrent Flow
Feed
Sl udge
(iii) Crosscurrent Flow
Clear liquid
FIGURE 2.6: THE DIFFERENT FL0\4 PATTERNS FOR LAfo1ELLA SEPARATORS
27
Clear liquid Feed
51 udqe
FIGURE 2.7: DUAL FLOH CLARIFIER
Clear liquid
Feed
51 udge
FIGURE 2.8: C:"'ARlrIER-THICKENER UNIT
28
2.2.1.2 Factors influencing the choice of flow pattern
The need to minimise the re-entrainment of particles into the
clear liquid stream and to ensure a continual and rapid removal of
particles from the plates are the main criteria influencing the
choice of flow pattern. Mathematical modelling by Probstein et
a1 48 ,49 suggests that for applications where high quality of super-co
natant is demanded the more stab le lurrent-supercriti ca 1 mode of
operation should be adopted. On the other hand, the influence
of sludge flow requirements is dependent on the type of sludge
being treated as well as the sludge volume fraction.
Studies by Forse1l and Hedstrom18 reveal that the cocurrent
flow design is particularly suited for light sludges with low
yield stresses in which the sludge volume is small. This is
because the cocurrent flow provides an additional drag force to
the reSUltant gravitational force to move the sludge layer. The
latter on its own may be insufficient to cause any movement. An
important application here is floc separation in connection with
the treatment of surface water.
For the heavy, finely dispersed sludges with small sludge
volume fractions, both flow patterns may be used. In practice,
however, the countercurrent flow is preferred because it implies
a much simpler and consequently less expensive design. The
clarification of circulating water used in wet scrubber plants is
an example that falls under this category of applications.
When suspensions with large sludge volume fractions are being
handled, the countercurrent flow principle is nearly always
29
advocated. The separation of biological flocs in the activated
sludge waste treatment process and the separation of metal
hydroxide on neutralisation of waste liquors from pickling plants
and the galvanic industries come under this category of applica
tions. A summary of the above recommendations are listed in
Table 2.1.
Sludge Volume Type of Sludge Fracti on Light, Network-Forming Heavy, Finely Dispersed
Low Yield Stress High Yield Stress
Low Cocurrent Countercurrent
High Countercurrent Countercurrent
. .
TABLE 2.1: FACTORS INFLUENCING THE CHOICE OF FLOW PATTERN
2.2.2 Hydraulic conditions
2.2.2.1 Laminar flow17 ,21,41,62
Laminar flow conditions must be established to ensure that
the sedimenting particles maintain a steady descent to the collec-are.
ting surface below, andAnot intermittently swept upwards by turbu-
lent currents generated within the sepa·rator. Non-turbulent
condition$.as characterised by a low Reynolds number for flow
through the separator, can be easily achieved by reducing the
hydraulic radius of the lamella channels. Moreover, to assist
in the development of laminar flow adequate provision must be
30
made to destroy the kinetic energy of the incoming stream to the
separator. In practice this is usually achieved by fixing an
impingement plate to absorb the impetus of the feed stream
just before it enters the lamella channels.
2.2.2.2 Even flow distributionll ,14,28
To use the total plate area efficiency the flow into the
separator must be distributed evenly between the plates as well
as width-wise across each plate. Otherwise, a bypass situation
will develop in which some parts of the separator will become
overloaded while others underloaded. Figure 2.9 shows a typical
arrangement whereby even distribution is achieved with the
installation of a distribution plate (with identical orifices)
at the top of the separator to remove clear liquid from each of
the plate spacings.
The principle is to create sufficient back pressure to force
the bulk content to distribute evenly over the entire volume of
the separator.
2.2.2.3 Environmental factor: adverse effect of temperature var;atlon
Any significant variation in the temperature of the incoming
stream to the separator can generate thermal and density currents
leading to the short-circuiting of flow. Such an effect was
detected by Little36 in a conventional clarifier where the
31
Orifice through which the supernatant is removed
Feed
1~~~J.~~~--- Distribution plate
. ... . .. : .. . . .... .. . ' . -+11--- Lamella plate
'~.' .. .. .. . . . .... .. • °0 ; ...
. '. . .
51 udge
FIGURE 2.9:. TYPICAL DE5IGtlll.RRAtIGEflENLFOR ACHIEVING EVEN. FLOW DISTRIBUTION
temperatures of the feed stream and the bulk content differed by
only about 2°C. In his subsequent work with a model tube separator
conSisting of five tubes the author was able to show that even when
the temperature of the feed stream was higher than the bulk content
by only O.2oC. very poor distribution of flow occurred with practi
cally all the flow passing up the first tube. The most effective
way of preventing this problem is to insulate the entire separator
unit, which should be feasible because of its compactness.
32
2.2.3 Geometric parameters
2.2.3.1 Plate spacing14 ,28
From a design standpoint, the plate spacing should be as
narrow as possible to allow the maximum number of plates to be
installed within a given separator volum~. This will drastically
increase the separator throughput vio an increase in the total
projected surface area available for sedimentation. However, the
lower limit on the plate spacing is governed by the potential
clogging problems and the re-entrainment of particles into the
clear liquid stream. Clogging problems are reported in the
literature to be frequent and severe in most waste treatment
applications but are practically non-existent in surface water
treatment. In a typical lamella thickener with plates of dimen
sions 0.5m by 3.4m ,the plate spacing is usually about
5 cm.
2.2.3.2 Angle of inclinationll ,l4
The angle of inclination must be sufficiently large to ensure
a continual and rapid removal of sludge formed on the plates.
Equally impor~ant, the plates must not be too heavily inclined to
cause the sludge layer to flow at too high a velocity capable of
forming of eddies which will result in its remixing with the
suspension layer.
inclination varies
For most applications the required angle of o 0 c from 45 to 50 (from the horizontal) depending
on the types of suspension being treated.
33
2.2.4 Feed entryll,l4,28,45
The present design strategy is to first introduce the feed
into a feedbox from which it gains access to all the plate
channels through feedports located a short distance above the
base of the plates. Figure 2.10 shows cl~arly such an arrange
ment in a countercurrent flow unit. Because the feed stream is
not introduced directly below the plates, the re-entrainment of
particles falling from the plates into the sludge collector will
be eliminated. Moreover the content in the feedbox will absorb
the impetus of the incoming feed stream, thus helping to sustain
laminar flow conditions within the plate channels.
2.2.5 Design of sludge collector28
High sludge concentrations are created in the sludge collector
by a further compression process that depends on surface loading,
detention time and the sludge bed thickness. In this respect the
lamella separator has a disadvantage because of the relatively
short sludge detention time. For finely dispersed mineral sludges
that disadvantage is commonly compensated by applying low amplitude
vi brati ons to enhance the compression process, as demonstrated in
Figure 2.11. In addition, the applied vibrations will improve the
flow characteristics of the sludges (mostly thixotropic in nature)
by lowering their apparent viscosities. With s1udges that form
loose networks a rake mechanism is normally used instead because
the compression process will be less affected by vibrations than
by direct agitation.
34
AD"''''''.' FLUM(a
1'''''''''''''''' TANK
FIGURE 2.10: COMMERCIAL COUNTERCURRENT FLOH LAMELLA PLATE SEPARATOR
BY PARKS ON CORPORATIOU
35
Sludge concentration
Vibrated sludge
Unvibrated sludge
FIGURE 2.11: EFFECT OF LOW AMPLITUDE VIBRATION ON COMPRESSION OF SLUDGE
The simplest design for a sludge collection and withdrawal
system is a hopper. In practice, a steep sided hopper (with a
side angle of at least 550 from the horizontal) is always
recommended. Shallow hoppers must be avoided because they tend
to rathole. Physically this means that more sludge is withdrawn
from the central parts of the hopper than along the walls. The
danger here is that the relatively stagnant layers near the walls
may eventually grow to fill the entire hopper thus rendering it
inoperable.
2.2.6 Design of settlingchannels
The shape and configuration of the settling channels are
important considerations for achi eYing optimum settl i ng charac
teristics. It is suggested by Beach4 that the settling distance,
as determined by the shape of the channels. be uniform so that
36
most particles have the same settling time. Circular tubes are
considered inefficient because particles entering at the top of
the tube have a greater distance to settle than those entering
at the sides. An optimum configuration is one that permits nesting
so that there is no wasted space between the channels in the sepa-
rator unit. Again, circular tubes are less efficient because of
the large amount of dead space between tubes in the array.
One design which is claimed to give optimum settling charac
teristics is the Chevron design developed by the Permutit Company.
The Chevron Tube Settler module is an array of nested 24-in. long
extended polystyrene tubes with a cross-section chevron shape
(see Figure 2.12). The manufacturer claims that the l-in. chevron
configuration has the highest perimeter of any common shape for
the same area; and the settling distance for particles entering
anywhere along the top of the tube is the same. The added advan
tage is that the V-groove promotes optimum sludge compaction and
flow. It is noted that the claims made above are based on semi-
empirical findings which have to be scientifically verified. The
reason being that there are a wide range of other commercial units
which use different configurations but claim to have advantages
of their own. The honeycomb cross-section tubes, inclined parallel . 27
plates and the inclined corrugated plates are some examples.
37
FIGURE 2.12: CHEVRON-DESIGN FOR SETTLING CHANNEL
2.2.7 Pretreatment of suspensions 14 ,3l
Coagulation and flocculation are steps commonly taken to
improve the settling characteristics of suspended matter during
the treatment of industrial water and process effluents. There
is usually an optimum dose of coagulant with which good clarifi
cation or thickening is obtained without incurring excessive
chemical costs or greatly increasing the volume or mass of sludge
for disposal. It is counterproductive to use excessive coagulant
because it can lead to charge reversal and stabilisation of a
suspension. Rapid and complete mixing of coagulant with the
water to be treated is important, particularly when using organic
polyelectrolytes which are fast acting.
Following the addition of a coagulant and flash mixing, it
is beneficial to provide a period of gentle mixing to promote the
growth of flocs (i.e. flocculation). ~lost commercial lamella
clarifiers and thickeners provide special compartments for this
purposE' in which the intensity of mixing is sufficient to promote
38
interparticle contact but insufficient to shear flocs that have .
been formed. The flocculated suspension must then flow gently
into the sedimentation tanks in a manner whereby the flocs are
not broken up.
2.2.8 Materials of construction7,14
The larger tanks are commonly constructed out of carbon steel
which is epoxy painted or coated with special material for
chemicals and physical protection. In some cases aluminium,
stainless steel and rubber-lined carbon steel are also used.
In contrast the smaller tanks are generally made of fibre glass
reinforced plastic (FRP). The small dimensions of the inclined
separators often make the use of specialised but expensive mate
rials feasible.
The most popular materials for lamella plates are the
different types of plastics. Different grades of FRP and polyvinyl
chloride (PVC) are commonly used, while stainless steel is the
generally preferred metal.
39
2.3 INDUSTRIAL APPLICATIONS
Lamella separators find wide applications particularly where
solid-liquid separation by pressure filtration is prohibited
owing to highly resistive. compressive filter cakes. They are
especially useful where the particle sett~ing rates are low. so
that unacceptably large conventional gravity separators have to
be used.
It is estimated that at present approximately 1000 inclined
plate separators are in use worldwide and about half of these are
located in North America (Janerus28). Inclined plate separators
vary considerably in design and size: installations range from
small package units of about la m2 of settling area to large
concrete basic installations of more than 100 m2 •
2.3.1 Water treatment
Applications in the water industry include sludge separators
and the incorporation of a pack of parallel plates in a pulsed
floc bed clarifier. Degremont15 claims that the use of lamella
plates imposes strict laminar flow on the behaviour of the liquid
stream as it passes through a bed of aluminium hydroxide floc. and
thus maintaining a stable bed. In addition. the use of pulsed
floc clarifier with lamella plates gives twice the value of flow
rates that were obtainable with more conventional designs.
40
The compactness of lamella separators has led to their use
in packaged skid mounted plants marketed by Anpress for the total
reclamation of water from vehicle washing process (Ward60). For
this particular application, a square section tube separator is
used inclined at 3So in a stop-start operation. Surface loadings
are reported at 0.48 m3/m2/hr based on tne effective settling area "
available.
Van Vliet57 describes a high lime clarification process in
which both inclined plate and tube modules are used to uprate a
conventional circular raked primary clarifier. Results show that
the efficiencies of the two modules are comparable and quite
insensitive to hydraulic loading in the range 3-12 m/hr. Because
of this the modules. are particularly useful as hydraulic uprating
agents for existing clarifiers and especially where uprating
factors of 1.5 to 2 would still ensure stable floc blanket
conditions.
It is found, from the literature, that for cocurrent flow the
required angle of inclination in water treatment is generally
300 _400 (from the horizontal) with a plate spacing of 35 mm.
The plates, because of their special design, are usually made
out of PVC. However, when operating countercurrently, the angle
is higher at 5So_600• This is because.the sludge layer now has
to slide against the shear force of the liquid phase.
41
2.3.2 Waste water treatment
The Water Research Centre6l have conducted extensive studies
on the application of inclined tubes or plates to sedimentation
tanks for waste water treatment. Their conclusion from working
with full scale tube modules in humus tanks is that the most
advantageous application is for uprating overloaded humus tanks,
but are not in favour of its use in primary tanks or for final
settlement in the activated sludge process.
Ironman26 describes a cross-flow separator which is being
used to clean up waste water from sand classification at a plant
in Austria. The plant is designed with a tank surface of 24 m2
handling 1150 m3/hr of water containing up to 100 tonnes/hr of
minus 0.5 mm solids. It is claimed to produce an overflow con
taining only 0.2 g/~ of solids and that all material above 0.063 mm
is retained.
The use of an inclined plate separator to clean up a chemical
effluent prior to a biological treatment process is reported by
Frick and Brown9. A countercurrent flow separator fitted with a
low amplitude vibrator for sludge compaction is described. The
total projected settlement area is 112 m2 for a surface area of
10 m2 , and the liquid flow rate obtained is 11.4 m3/hr.
A similar design of inclined plate separator is described by
York67 in an application to the removal of sludge from 40% phos
phoriC acid. The effectiveness of the lamella separator is compa
rable to a conventional raked tank separator with a nozzle discharge
disc centrifuge. Some pilot plant work (using an inclined plate
device with a total projected area of 70 m2 at an angle of incli
nation of 45°), on a feed stream containing 3% (wt) of solids is
reported to produce an overflow rate of 10 m3/hr with a solids
content of 0.5%. The underflow solids concentration was found
to be about 12 to 15%.
Inclined'plate and tube separators are also being applied
to oil-water separation by CJBD Ltd21 , William Boulton Ltd.
Pielkenrood-Vinitex N.V. ~nd Anpress.
2.3.3 ~1ining
The main areas of application of lamella separators to the
mining industry lie in the clarification, thickening and fine
classification of ores. As examples: the treatment of waste
water in underground mines; thickening of solids between milling
systems and flotation plants; thickening of tailings and concen
trates; and the improvement to water clarity in dressing plants.
A further effective use of the inclined surfaces is in
equipment for dissolved air flotation. The advantages it has
over the more conventional designs are the added separation
surface and better hydraulic control. Plants using this principle
have already been developed by CJBD and Anpress.
43
2.3.4 TABLE 2.2: SURFACE LOADINGS ON TYPICAL APPLICATIONS
Type of Separator
Tube
Tube
Tube
Tube
Inclined plate
Inclined plate
Inclined plate
Cross-flow
Square tube
Appl i cati on
Al (OH)3 floc in water
Humus tanks
Activated sludge
Humus tanks
High lime clari fi cati on/ water
Chemica 1 effl uent
Phosphoric acid sludge
Sand fines from water
Total recycling vehicle wash water
Surface LoadinQ
(m3/m2/hr)
30
10-13
1.5
1.2
3-12
(0.10)
(0.14)
4.7
(0.48)
Note: The figures quoted above are based on free air/liquid
surface areas except those in brackets. which are
based on projected areas.
44
2.4 ADVANTAGES AND DISADVANTAGES OF LAMELLA SEPARATORS 28 ,56
This section is meant to highlight the major advantages
and disadvantages of a lamella separator compared to a conven
tional vertical separator.
2.4.1 Advantages
2.4.1.1 Lower capital and operating costs
Users of lamella separators can expect to have the benefits
of lower capital and operating costs because of reduction in land
use and the potential of higher separating efficiencies. The
space requirement for an inclined plate separator is often only
10% or less of the land area needed for a conventional vertical
separator.
2.4.1.2 Higher separating efficiency
This is because a lamella separator can provide nearly
quiescent conditions within the settling channels, thus eliminating
the effects of flow currents which may impede settling and cause
short-circuiting. Lamella thickeners are now known to produce
high sludge concentrations which were previously not achievable
with the use of conventional thickeners.
2.4.1.3 Convenience of construction and installation
The separator units are usually fabricated in plastic and
metal in factories so reducing the inconvenience and costs of
on-site work. Moreover, because the materials of construction
45
are light weight, it is possible to install such separators on
high locations in buildings.
2.4.1.4 Fewer maintenance problems
There should be a reduction in maintenance problems because
there are fewer moving parts that require maintenance and that
may malfunction.
2.4.2 Disadvantages
2.4.2.1 Short sludge detention time for compression
The relatively short detention time for the sludge in a lamella
separator is a disadvantage in applications where high sludge con
centrations are created by long periods of compression. Consequently,
in practice, low amplitude vibrations are applied to enhance the
compression process.
2.4.2.2 Susceptibility to fouling problems
Not recommended for applications with large scaling potential
(especially not where the scale cannot easily be removed) and
sticky solids which can cause plate fouling due to their clinging
tendencies. Lamella separators are particularly vulnerable to this
fouling problem because of the presence of large number of plates
and small plate spacing.
46
CHAPTER 3
EXISTING DESIGN METHODS FOR LAMELLA SEPARATORS
3.1 EMPIRICAL APPROACH •••
3.2 SEMI-EMPIRICAL APPROACH
3.3 THEORETI CAL APPROACH
47
Page No
48
50
52
CHAPTER 3
EXISTING DESIGN METHODS FOR LAMELLA SEPARATORS
The eXisting sizing methods for lamella separators can be
placed under three main categories in accordance with the approa
ches taken, i.e. the empirical, semi-empirical and theoretical
approaches. The main objective is to determine the total surface
area required for sedimentation to achieve the desired separator
throughput. These design approaches are discussed individually
in the following order.
3.1 EMPIRICAL APPROACH
Janerus 28 has described a sizing method for inclined plate
clarifiers based wholly on experimental data from column settling
tests. Results of the settling tests12 are regarded as representing
the performance of an ideal clarifier. To simulate the relatively
short detention time in a plate clarifier, the settling tests are
usually performed in a 500 ml graduated cylinder (of the same
geometry), from which a fixed volume is withdrawn from the top
after a set time to simulate a certain loading rate. The depth
of the top volume that is withdrawn is chosen to correspond to
the plate distance intended for the actual design.
From the results of the settling tests a relationship is
then established between the overflow clarity and the surface
loading rate, which for a desired clarity and corresponding flow
rate, gives the necessary projected area. In practice, however,
48
and depending on the design, a safety factor of between 1.25 and
2 is normally added to the projected area to allow for non-ideal·
hydraulic conditions and any expected variations in the settling
properties. To complete the design, other specifications such as
the plate inclination, plate length, plate width, the feed and
withdrawal arrangements etc. are generally' specified independently
based on the experience and recommendations of the manufacturers.
In retrospect this empirical approach suffers from at least
two serious drawbacks:
a) extensive tests, which are both laborious and costly, have
to be conducted to provide reliable data and thus avoid the
use of undesirably large safety factors for the predicted
surface area requirements. Moreover, the settling tests are
difficult to perform because the test samples and hyraulic
conditions must be reproducible and also be representative
of the actual full-scale application.
b) the independent considerations placed on the specification of
most design parameters are by nature oversimplistic, and
consequently vulnerable to the folly of underdesign or over
design conditions.
The need to alleviate the problems above led to the deveiop
ment of a semi-empirical approach, which incorporated a theoretical
basis to describe the functionality of some ruling parameters.
A few notable sizing methods that come under this category are
described in the following section.
49
3.2 SEMI-EMPIRICAL APPROACH
Graham and Lama20 have developed a sizing method for an
inclined thickener based on the assumption that its design over
flow is the sum of the overflow calculated for a vertical thick-
ener (having the same free air/liquid interfacial area) by the
Coe and Clevenger method and the additional overflow produced at
the inclined surface. The latter is derived using only the rate"
enhancement term (i .e. the second term on the right) in the
Nakamura and Kuroda equation, written as:
_ ~ = Fv (1 + h COSCL) ut b Eqn.(3.l)
As discussed in Section (2.1.1), F is an empirical coefficient to
account for the discrepancy between theory and experimental data.
Details of the mathematical derivations are fully described in
their paper and will not be reproduced here.
Application of their proposed sizing method, however, showed
discrepancies of up to 46% between the predicted and measured
thickener capacities. It is useful to note that their experiments
were conducted in an inclined thickener comprising of two plane
surfaces 44 in. by 96 in.at 2.3 in. separation and inclined at
500 from the horizontal. Suspensions of precipitated calcium
carbonate in water at concentrations ranging from 15.1 to 54.2 grams
per litre were used. The empirical coefficient, F, was found to be
a function of solids concentration of the feed (ranging from 0.5
to 0.7), but in their calculations a fixed average value of 0.56
50
was used. The authors concede that their sizing method is only
useful in obtaining a first approximation of thickener capacity.
An alternative method has been developed by Zahavi and
Rubin70 based on the addition of terms to the well-known Yoshioka
flux curve method, which is commonly useq to estimate the area
requirements of conventional thickeners. The method states that
for a continuous inclined separator, its solids flux represented
by (Gc)p may be assumed as the sum of the solids flux in the same
continuous separator but without inclined surfaces (Gc) and the
additional solids flux contributed by the inclined surfaces
i.e. (G) : G + G c p c p Eqn. 3.2
Applying the yoshioka technique, the authors then plotted solids
flux versus concentration curves for Gc and Gp to obtain a limiting
solids flux value, (GL)p' to provide the basis for design calcu
lations. In principle (GL)p represents an upper limit and corres
ponds to the maximum allowable design solids flux. The authors
conclude that their sizing method is in practice only about 55%
accurate, though still within the commercially accepted design
safety factor.
It is evident that although the semi-empirical sizing methods
developed by Graham and Lama and Zahavi and Rubin are incapable
of providing sufficiently accurate predictions of the separator
capacities. they do indicate the possible directions for improve-
ment to the overall design criteria for a continuous inclined
separator. 51
3.3 THEORETICAL APPROACH
Two strategies have been adopted to develop design methods
based on theoretical considerations. The first assumes that
all particles settling in a lamella channel behave independently
of each other and thus possess unhindered .trajectories of their
own. A summary of all the particle trajectories that start and
end within the length of the lamella channel is then used to
calculate the required surface area to achieve a desired effi
ciency of particle removal. In principle this assumption can
only be justified in dilute suspensions where the particles
experience unhindered settling behaviour.
The second strategy is adopted to handle hindered settling
conditions where all the particles interact with one another to
produce an overall settling behaviour. As such, the suspension
is now treated as a continuum settling under the action of
gravity. Details of design methods developed from these strat
egies are in turn discussed below.
Ward60 has developed a design equation to estimate the area
of lamella separator for dilute sedimentation applications based
on residence time considerations. The author starts by considering
a particle on a limiting trajectory entering the separating zone
at point A and being captured at point B on the lower inclined
surface, as shown in Figure 3.1. By assuming plug flow conditions
in the settling channel the residence time for the particle in
the separating zone is obtained from the following equation:
52
where Q = volumetric flow rate through the separator,
n = number of settling channels,
L = length of plate,
b = plate spacing, and
W = width of plate
Eqn.(3.3}
To supplement the use of Equation 3.3 in the final analysis another
equation is formulated to relate tR to the suspension property
using the modified Nakamura and Kuroda equation, i.e.
tR = vertical distanced travelled b¥ the particle alon~ the trajectory enhanced part1cle settling veloc1ty
= __ ...l.(.::;b /c..:C~o s;::a~}-,.-;:-;:-,.,+ [ 51na Cosa}
b F v (1 Eqn.(3.4}
where F is an empirical coefficient to account for inaccuracy of
the Nakamura and Kuroda equation, and
L Sina replaces h in the original equation.
The two residence times are then equated to produce an expression
relating the required lamella plate area to the desired separator
throughput, i.e.
53
FIGURE 3.1: LIMITING TRAJECTORY FOR SETTLING PARTICLE
WLn =
r required lamella pI ate area
Q
F v ( 1 + L_S.:...l:.;.nrb_c:,,:o.,::.s CL::.) CO SCL Eqn.{3.5)
The settling velocity v, and the empirical coefflcient. F. are
usua1ly determined experimentally. From the literature19 •Z0 , P
is found to be a function of concentration for Ji fle-rU\\- $uspen-
sions ·and varies between 0.5 and 0.7 over a large range of concen-
trations likely to be encountered in most industrial applications.
Based on this residence time approach other more complicated
models have been devised by various researchers to take into
54
account different vessel shapes63 ,64 and the actual liquid flow
profile and thickness of sludge accumulated in the settl ing
channe1 40 ,59,63,64.
The earliest attempt to apply a theoretical analysis to
lamella sedimentation under hindered settling conditions was
made by Jernqvist30 The principal objective was to develop a
design method for predicting the maximum capacity of a lamella
thickener. Two major assumptions were made in his development:
i) that the settling rate is solely a function of the local
concentration and any differences of horizontal concentra
tions are assumed to be momentarily levelled, and
ii) that the thickness of the clear liquid layer beneath the
upper inclined surface and the thickness of the sludge layer
on the lower inclined surface are negligibly small.
Furthermore, the author defined three steady-state conditions
that may exist in a lamella thickener, and which were subsequently
used in the theoretical analysis:
I) where the interface between the clear liquid and the suspen
sion is at the level of the feed inlet, as shown in Figure
3.2(a). The bulk suspension is assumed to be homogeneous
and at high concentration.
Il) where the interface between the clear liquid and the suspension
is again at the level of the feed inlet. However, a discontinuity
between low and high concentration regimes exists in the bulk
suspension (see Figure 3.2(b», and
55
..
(al Clear liquid
(b)
Clear liquid
Feed
Low cone.
Sludqe
( c)
l:lear liquid
Feed
FIGURE 3.2: STEADY -STATE CONDITI ONS PROPOSED BY Jf fU;:JV I ST
56
Ill) where the interface between the clear liquid and the sus- .
pension is above the feed inlet. As shown in Figure 3.2(c),
the location of discontinuity between the low and high
concentration regimes is at the level of the feed inlet.
By constructing material balances for each of the steady-state
conditions, based on the initial assumptions regarding the sus
pension properties, expressions were obtained to describe the . concentration distribution and solids fluxes along the entire
length of the lamella thickener. These expressions were then
used to calculate the maximum thickener capacity. It was found,
from plots of solids flux versus concentration curves, that
lamella thickening, under the conditions of the analysis, is
in fact a special case of vertical thickening. This design
method suffers the drawback that it may only have limited,'
industrial applications because of the ad-hoc assumptions made
regarding the settling behaviour and steady-state conditions
that may exist in a lamella thickener.
A more general design method has been proposed recently by
Probstein and his co-workers. In it a design equation is deve
loped to estimate the capacity of a lamella separator based on
expressions of velocity fields for the different settling zones
that exist in the settling channel. Further details on the
mathematical model that is devised to establish the velocity
fields are already discussed in Chapter 2.
57
CHAPTER 4
DEVELOPMENT OF DESIGN METHODS
4.1 INTRODUCTION
4;1.1 Evaluation of the existing design methods 4.1.2 Research objectives
4.2 DESIGN-CONSTRAINTS .,.
4.2.1 Steady-state constraint 4.2.2 Larninar flow constraint 4.2.3 Flow stability constrai~t 4.2.4 Sludge flow constraint
4.3 SIZING METHOD
4.' PROPOSED DESIGN SCHEME . . .
58
...
Page No
59
59
60
62
62 76
78 83
85
88
CHAPTER 4
DEVELDPMENT OF DESIGN METHODS
4.1 INTRODUCTION
The purposes of this chapter are to establish the potential
areas in which improvements to the design of a lamella separator
can be made and to describe the proposed research programme for
achieving those aims. Before that an evaluation of the existing
design methods which leads to the derivation of the present
research objectives will be covered.
4.1.1 Evaluation of the Existing Design Methods
Despite the significant rejuvenation of interest in lamella
separators in recent years, the existing design methods are still
limited in their extent and in their accuracy - this is particularly
so in thickening applications. It is evident that process engineers
currently specifying this equipment do not have reliable design
methods and have to resort to extensive pilot plant trials to fina
lise their design specifications. The more well tested design methods
that have been reported in the literature are only about 50% accu
rate in predicting the required separator capacities. Even the
relatively recent design methods developed by Probstein and his co
workers. which are based on a dynamic flow model, give no better
agreement between the predicted and experimental separator capaci
ties. Though these authors attribute the discrepancy largely to
stability problems and mixing, it is evident that the models them-
59
selves have inherent weaknesses because of too many ad-hoc assump
tions. For instance, the authors simply assume the existence of
steady-state stratified layers in the settl ing channel s, whi ch
Acrivos and Herbolzheimer have since shown do not exist in all
cases. In practice the shortcomings of the existing design methods
have also given rise to two common but serious problems: the
excessive contamination of the supernatantwith re-entrained parti
cles from the suspension layer and the frequent inability to achieve
the designed level of sludge thickening.
It is therefore the aim of this research programme to seek
remedies for the deficiencies highl ighted above and to establish
some design guidelines and strategies to apply to lamella separators.
4.1.2 Research Objectives
The principal objective is geared towards improving the funda
mental understanding of the different aspects of inclined sedimenta
tion. This will provide a basis for developing the means of predic
ting and interpreting the. overall settling behaviour in a continuous
system. The following constraints which are deemed to be essential
for the successful operation of a continuous separator will be
studied in further detail to produce design guidelines for the
purpose of sizing:
i)
ii)
Steady-state constraint) )
Laminar flow constraint)
60
to ensure the formation of steady-.
state stratified viscous layers in
the settling channel.
..
iii) Flow stability constraint) to minimise the re-entrainment of
) particles from the suspension layer
) into the clear liquid layer, and
iv) Sludge flow constraint ) to ensure a continual removal and
) rapid removal of sludge formed on
) the lower inclined surfaces.
It is also intended to establish optimum operating conditions
to provide a foundation for the future development of an optimisa-
tion procedure for lamella separator design. It is believed that
there exists at least two optimum design variables: an optimum
angle of inclination and an optimum aspect ratio.
Another objective is to establish a sizing method for lamella
separators that is capable of predicting the area requirements as
well as providing the range of conditions over which it is appli
cable. However, the conditions of application as provided by the
theoretical models will have to be verified experimentally.
Finally, a more comprehensive design scheme which incorporates all
the relevant design variables and constraints will be developed.
It is believed that by imposing constraints on the design variables
to avert the creation of non-ideal conditions the overall design for
a lamella separator can be substantially improved.
Details of the various aspects of lamella separator design
that will be covered are given below.
61
4.2 DESIGN CONSTRAINTS
4.2.1 Steady-State Constraint
A prerequisite of the continuous operation of a lamella sepa
rator is the attainment of steady state. In most existing design
methods, such a condition is assumed to be inherently attainable.
An example of the latter is the formation of steady-state stratified
viscous layers within the settling channels.
However, recent findings by Acrivos and Herbol zheimer2,3 have
shown that such an assumption is in fact oversimplistic in nature,
and hence, vulnerable to folly because the formation of steady
state stratified layers does not occur in all cases. The authors
have discovered that. though in a low aspect ratiot separator the
assumption of steady-state is in fact valid, in the case of a high
aspect ratio* separator, there may be constraints on the dimensions
and design of the separator that will need to be satisfied before
steady-state conditions can be achieved. The authors have reported
to obtain excellent agreement between their theoretical and experi- ,
mental results.
It is our intention to further verify those steady-state
constraints, both theoretically and experimentally. before applying
them to the proposed scheme for improving the overall design of a
lamella separator. The flow models that have been developed by
t A low aspect ratio separator is one in which the vertical height is of the same order of magnitude as the channel spacing (i.e. h/b = 0(1))
* On the other hand. a high aspect ratio separator is one in which the vertical height is much greater than the channel spacing.
62
Acrivos and Herbolzheimer to establish the necessary conditions
for the formation of a steady state clear liquid/suspension inter
face in both the low and high aspect ratio vessels will be dis
cussed below.
4.2.1.1 Theoretical development of Acrivos-Herbolzheimer's Models
For the purpose of clarity, the steps in which the flow models
are developed (i.e. based on the principles of continuum mechanics53,54)
are summarised as follows:
Step 1: Formulation of the appropriate dimensionless ensemble
averaged momentum equations.
Step 2: Determination of stretched variables*.
Step 3: Introduction of stretched variables into the momentum
equations.
Step 4: Simplification of the momentum equations - by neglecting SUbOT'Qlno\e
terms"to the leading order ones.
Step 5: Introduction of boundary conditions.
Step 6: Solution of simplified momentum equations.
4.2.1.1.1 General formulation of momentum equations
The appropriate equations of motion for the settling system
are derived from the ensemble-averaged of the momentum equation
* The object of using a stretched variable is to demonstrate the order of magnitude of that variable - e.g. a variable i is written in terms of its stretched variable i as:
i = [I1T, where the bracketed value gives its order of magnitude.
63
based on the following assumptions:
i) the flow is laminar,
ii) the Reynolds stress terms relative to the bulk stress may be
neglected, since the Reynolds number based on the flow around
the particles is assumed to be small (this assumption is
reasonable in most systems of practical interest because of
the small size and slow settling velocity of the sedimenting
parti cl es) •
iii) the suspension behaves like a Newtonian fluid with an effective
viscosity which is a function only of the local concentration
of the particles.
iv) the fluid and particles are assumed to be incompressible, and
v) the suspension is assumed to be homogeneous.
With these assumptions, the appropriate ensemble-average momentum
equation, written in dimensionless form becomes:
Eqn. 4.1
where p(~) = effective density of the suspension divided by that
of the pure fluid p
= 1 + co~ (-; - 1)
AI(~) = effective viscosity of the suspension divided by that
of the pure fluid
P = dimensionless kinetic pressure
= dimensionless absolute pressure, p, minus the dimension-
less hydrostatic pressure head due to the suspension of
concentration, co~
fi4
'Jp = 'Jp
= 'Jp - A(l + -;----T- P e Co\pp-p)
$ = local particle concentration divided by the initial con-
centration of suspension. co . ... e = unit vector in the direction of gravity
U = dimensionless bulk average velocity
R = dimensionless Reynolds number phvo =--
jJ
A = sedimentation Grashof number divided by the sedimentation
Reynolds number
gh Z (p - p)c-= p 0
\lVo
It is important to note that all the terms in the above equation
are made dimensionless in the following manner:
a) all velocity terms are made dimensionless with Vo (the average
settling velocity of an individual sphere in a suspension with
volume fraction c, in a vertical vessel). o
b) all position coordinates with h (the characteristic length of
the macroscale motion. which Acrivos and Herbolzheimer have
taken to be the initial height of suspension).
c) density with P. the density of pure fluid.
d) viscosity with P, the viscosity of pure fluid
e) time with h/vo' and
f) pressure with vop/h
Because of the definition for P in Equation 4.1, the body force ..,..
in the settling system appears as a buoyancy term .. , - 1\(1 - ~)e.
In the vast majority of cases, A is 0(10 5 ) or larger - particularly
if h is set equal to the initial height of the suspension - and
hence the authors pursued the asymptotic solution of Equation 4.1
as 1\ ..,.~. Under these conditions the buoyancy term in Equation 4.1
clearly plays an important role. This term vanishes within the bulk
of the suspension where ~ = 1, but is large within the clear-liquid
layer underneath the upper inclined surface where it induces strong
velocity currents. Equation 4.1, which has just been described,
will now be used to develop the flow fields in a low aspect ratio
vessel.
4.2.1.1.2 Development of flow fields in a low aspect ratio vessel (i.e. h/b - 0(1»
Since it is anticipated that the thickness of the clear liquid
layer will become vanishing1y small as A ..,. ~, it is deemed convenient
to introduce the boundary layer coordinates (X,Y) with X denoting
the coordinate along the upper inclined surface and Y, the coordi
nate normal to.it. The corresponding velocity components are U and
V, as illustrated in Figure 4.1.
/----- Upper inclined surface
____ Clear liquid layer
~~----Interface
--~--- Suspension layer
X=O
., .. ,
FIGURE 4.1: COORDINATE SYSTEM SHOWING THE VARIABLES USED IN.THE ANALYSIS OF FLOW MoTIoN IN A Low ASPECT RATIO VESSEL (pARALLEL pLATE)
Step 1: Formulation of the appropriate ensemble-averaged momentum equation
In the clear liquid layer, where q,. = 0, p(~) = 1, )l(q,) = 1,
the general ensemble-averaged momentum Equation 4.1 is reduced to
which is written in terms of the X and Y components as:
R {ilU + U ilU + V ilU} = _ ~Px + ACose + {a 2u+ il2U} TI ax av a aX2 ay2
and
R {ilV + U ilV + V av} = TI all aY"
67
Eqn. 4.2
Eqn. 4.3
Eqn. 4.4
Step 2: Determination of stretched variables
The aim in this part of the mathematical development is to deter
mine the orders of magnitude of the velocity components U and V, and
the clear liquid layer thickness, Y.
Because the motion of the interface between the suspension layer
and the clear liquid layer is determined by that of the particles resi
ding on it (and since all velocity terms are made dimension1ess with
vo' the settling velocity of the particles), the dimension1ess velo
city component V must be 0(1) along the interface - and hence, it is
similarly 0(1) within the clear liquid layer.
i . e.
In turn, this implies from the equation of continuity
aU + aV - 0 3)(* aY"- Eqn. 4.5
that the longitudinal velocity U is, in order of magnitude, inversely
proportional to the thickness of the· clear· liquid layer Y. Moreover,
since the clear liquid layer thickness is anticipated to be vanishing1y
small as A + 00, U is expected to be correspondingly large and the lea
ding viscous term will be· a2U• Since, on account of Equation 4.2
ay2 the viscous forces must balance the buoyancy force (O(A)), .the order
of magnitude of U must be O(A1 / 3 ) and Y = O(A- 1 / 3 ).
The fon owing stretched vari ab 1 es can therefore be defined
* For a parallel plate lamella separator, the length scale in the X-direction is 0(1).
68
.: ....
"
Eqn. 4.6
Step 3: Introduction of stretched variables into the momentum equatlOns
By introducing the stretched variables, Equations (4.3) and
(4.5), become:
a (A l/3U) a(A -1/3V')
= _ ap + ACose ax
which with simplification and rearrangement becomes
and
2'" !J!. + Cose aY'2
'" '" au + ~ = 0 ax ay
Eqn. 4.7
Eqn. 4.8
Step 4: . Simplification of momentum e~uations by neglecting terms that are small compared to t e leading order ones
Since in this analysis, A is taken to :be asymptotically large,
all terms less than A- 1/ 3 will be neglected and Equation 4."J is
simpl ified to
69
0' •
a2~ + Cose = 0 '" ay2
Eqn. 4.9
The pressure term in Equation (4.1) is also neglected because it
can be shown that P is at most 0(A2/3) within the clear liquid
layer. The mathematics leading to this conclusion are too involved
and will not be presented here - details can be found in the original
paper of Acrivos and Herbolzheimer.
Step 5: Introduction of boundary conditions
The following boundary conditions will be used to solve
Equation (4.9) to give the longitudinal velocity U.
at ~ = 0
(i.e. zero liquid velocity at the walls)
ii)
Eqn. 4.10
Eqn. 4.11
(this velocity gradient is obtained by matching constancy
of shear at the clear liquid/suspension interface).
Step 6: Solution of simplified momentum equations
a) Velocity components. U and V
The longitudinal velocity component ~ is obtained by integrating
Equation (4.9) and using the boundary conditions (4.10) and (4.11)
i.e. U = Coss (V' ~- l ~2) + O(A -1/6)
rO
70
Since A is asymptotically large the equation above can be simplified
to
:v '" '" '" u • Cose (Y 5- i y2) Eqn.4.12
On the other hand, the normal velocity component ~ is obtained vi~
the continuity Equation (4.8) in the following manner:
Differentiating Equation (4.12) with respect to X,
'" '" au'" a<5· ax = Y Cose ax
and hence,
'" '" ~ = _ ~aU = - y Cose a'S' aY "A . ax
The latter is then integrated to give
'" '" '" y2 3<5 V = - a;- Cose ax
'" b) Solution for clear liquid layer thickness <5
Eqn. 4.13
'" The solution for the clear liquid layer thickness <5 is obtained
via the following kinematic condition at the clear liquid/suspension
interface i.e.
"V "". .
A -1/3 aT<5 + U .M - ~ = Sine at Y = 6' a aA . Eqn. 4.14
71
The above equation is essentially a mass balance describing the
.rate of growth of the clear liquid layer as a function of the
influx of liquid through the interface and the net flow rate of
liquid along the clear liquid layer itself. Substituting ~ and ~
into Equation 4.14 the latter becomes:
'" '" A -1/3 ~ + Cose &2 ~ = Sine aT ax Eqn. 4.15
Equation 4.15 is then solved by the standard method of characteristics
(Ref 2) to determine the time-dependent behaviour of the flow \~ithin
the clear liquid layer. The solution that is obtained is that at
any fixed position X along the upper inclined surface, the clear
liquid layer thickness, 5, increases linearly with time until it
'" actually reaches a steady-state value and then after 0 remains
steady and independent of time. The equation for the steady-state
c1ear'liquid layer thickness at any position X is given by
(&) - (3 X tane)I/3 steady - Eqn.4.16 state
From a design point of view the above result is significant in
two ways: firstly, it establishes the feasibility of operating a
low aspect ratio separator on a continuous basis since the condition
of steady state is easily achieved; and secondly, it permits the use
of the existing design methods - such as those proposed by Probstein
and his co-workers - in which the ad-hoc assumption is made regarding
the existence of steady-state stratified viscous layers within the
settling channels.
72
4.2.1.13 Development of flow fields in a high aspect ratio separator (i.e. h/b = O(A1/ 3))
Using the same mathematical approach as described in the previous
section, we have also verified theoretically the flow fields deve-
loped by Acrivos and Herbolzheimer for describing the behaviour of
the clear liquid layer in a high aspect ratio separator. However,
because the mathematics involved is rather tedious the detailed
development will not be presented ··only the main points that are
of significance to the design of a continuous system will be dis
cussed.
The flow fields developed for both the batch and continuous
settling systems will be dealt with in turn.
In the batch settling system, it has been found that, unlike
the previous case with the low aspect ratio separator, the clear
liquid layer that is formed along the length of the separator
attained steady state only below a certain critical point - above
that the thickness of the clear liquid layer is in transient and
increases rapidly with time until it occupies the entire channel
spacing (this effect is illustrated in Figure 4.2).
Discontinuit Xc
X=O .
FIGURE 4.2: BATCH SETTLING BEHAVIOUR IN A HIGH ASPECT RATIO SEPARATOR
73 /
The relevant equations that have been derived to predict the
steady-state section of the clear liquid layer and the critical
position of discontinuity are given below:
~ ~
(o)steady state
= ~ (1 - 11 - ~ (3 X tane)1/3) 2 B
where 6 =A1/ 30 , and
B =A1/3B
Position of discontinuity,
.'
Eqn. 4.17
Eqn. 4.18
Hence, in view of the batch settling behaviour, the feasibility
of using high aspect ratio separators for continuous systems is open
to question because it is far from obvious that steady state condi
tions are attainable under all sets of operating conditions. However,
it has been found that in a continuous system the transient behaviour
that is described above can in fact be suppressed, but, only if the
feed and withdrawal arrangements and/or the separator dimensions
are properly chosen. Thus, in principle, it is possible to attain
steady state conditions for all values of the aspect ratio. Examples
of such design constraints that apply to the more common modes of
operation are summarised below:
74
I) Cocurrent flow
In order to ensure that steady state conditions are attainable
under all sets of operating conditions it is required that
'" B3;. 192 tane X
Moreover, in line with the above constraints, two possible modes
of operation can be used, i.e. the subcritica1 and the supercritica1
modes.· The latter is in fact consistent with the earlier findings
by Probstein and his co-workers (Ref. 4B).
11) Middle feeding
Steady state conditions are only attainable provided that a
significant portion of the feed, or all of the feed, is added below
the position of discontinuity (Xc) in the corresponding batch process.
Ill) Countercurrent flow
Since all the feed is introduced below the point of discontinuity
(as prescribed in Case 11), steady state conditions are attainable
under all sets of operating conditions. No additional constraint
on the separator dimensions·is necessary.
Overall Consideration
It is important to note that the design considerations that have
been discussed so far are strictly applicable to a dilute settling
75
system because that is the condition under which all the flow
models have been developed. However, it is believed that even
at higher concentrations the important predictions regarding the
qualitative behaviour will remain unchanged. In particular, the
existence of discontinuity in a batch settling system and the
corresponding need for steady state constraints in a continuous
system.
It is our intention to verify these theoretical predictions
experimentally and to establish the limitations witlilRwhich they are
applicable. It is believed that useful guidelines can be derived
for design purposes.
4.2.2 Laminar Flow Constraint
Operating a lamella separator under laminar flow conditions is
essential for two main reasons: firstly, it is a·pre-requisite for
the.formation of steady-state stratified layers; and secondly, it
ensures that even at the maximum designed flow rate the sedimenting
particles maintain a steady descent to the collecting surface below, are
andl\not intermittently swept upwards by turbulent currents generated
within the separator. Consideration is given below to establish the
required constraint on the separator dimensions in order to achieve
laminar flow conditions.
From a design standpoint, a non-turbulent condition as charac
terised by a low Reynolds number for flow through the separator, can
be easily achieved by reducing the hydraulic diameter of the settling
76
channel given by the equation below,
i .e. (Re) = p v D laminar jl
flow
where v = velocity of fluid flow
p = density of fluid
~ = viscosity of fluid, and
D = hydraulic diameter of the settling channel
4 x =--~~~~~~~~~~~~~~~~~~
Eqn. 4.19
For the purpose of this research which is concerned with the use of
a parallel plate lamella separator of channel width, W, and channel 2Wb spacing, b, the hydraulic diameter is given by (W + b) •
Therefore, equation (4.19) can be rewritten as:
(Re)laminar flow
= 2pWbv (w + b)l! Eqn. 4.20'
It is a rule of thumb that the Reynolds number should always be
less than 2000 to avoid non-laminar conditions, though for greater
safety a lower limit of 50041 has been cited. Using the lower limit
of 500, Equation (4.20) can noW be rewritten in constrained form as:
2pWbv (w+bh < 500 Eqn. 4.21
Q If v is represented in terms of the actual flow rate as WD' then, by
77
substitution into Equation (4.21) gives
2pQ (w +b) \l < 500
which can be rearranged to give
(W + b) > ~~O)l Eqn. 4.22
Hence in the actual design the provided channel width must be at
least equal to or greater than that imposed by Equation (4.22) in
order to achieve laminar flow conditions. On the other hand, its
upper limit is governed by the need to achieve good distribution of
flow across the entire width of the settling channel. It is gen
erally accepted that for this .purpose the channel length to channel ~~
width ratio should be at least 5 to 1. The channel spacing, b,
is normally specified independently based on potential clogging
prob 1 ems.
4.2.3 Flow Stability .Constraint5,25,34,38,66
One of the major problems arising from a lamella separator is
the contamination of its supernatant with the particles re-entrained
from the suspension layer. This has, in practice, led to substan
tial reductions in the overall separation efficiencies. It is the
intention here to first highlight some of the current design strat
egies that are used to overcome this problem, and subsequently to
suggest ways in which improvements can be made.
78
It has been shown by Probstein and his co-workers that
currently operated lamella separators, i.e. those operating in
the countercurrent and cocurrent-subcritical modes are inherently
susceptible to particle re-entrainment because of the existence of
a part of the suspension layer which is relatively unstable and
moving upward at high velocity with the clear liquid stream -
an illustration of this effect is given in Figure (4.3) •
Inter
. '
Clear liquid layer
face ----~--:
Cl
~Unstable suspension layer just adjacent to the interface
---r:----- Suspension layer
FIGURE 4.3: TYPICAL VELOCITY PROFILE FOR THE COUNTERCURRENT AND COCURRENT-SUBCRITICAL MODES OF OPERATION
Hence 'the problem is expected to be particularly severe when treating
polydispersed suspensions because the smallest particles will
inevitably find their way into the unstable region and subsequently
get re-entrained. To avert this problem the authors proposed
switching over to a cocurrent-supercritical mode of operation which
79
has a more favourable velocity field. As shown in Figure (4.4).
part of the clear liquid layer just adjacent to the suspension/
clear liquid interface is actually dragged downward in the direc
tion of the settling suspension thereby helping to stabilise the
interface and also the particles around that region •
...,...,;~---Suspension layer
Clear liquid layer -------:-r-
Interface
FIGURE 4.4: TYPICAL VELOCITY PROFILE FOR THE COCURRENT-SUPERCRITICAL
MODE OF OPERATION
There is another cause of particle re-entrainment which is
perhaps more difficult to control and that is due to flow instability
brought about by wave disturbance at the clear liquid/suspension
interface.
80
Based on current knowledge there is no reliable design method
available which can be used to suppress the effect of flow insta
bility, though in the literature some initial work has been under
taken by Leung34 • Working with the supercritical mode of operation,
the author attempted to characterise the unstable nature of the
interface between the clear liquid layer and the suspension layer
as a function of settler angle and feed rate. It is shown that at
low settler angles (i.e. a < 100 from the horizontal) the destabili- .-
sing mechanism is associated with an inflectional point in the flow
due to shear; and at high angles (i.e. 100 < a < 600), with a
gravity destabilising mechanism. The former, however, is not rele-
vant to most industrial applications because the range of angles
covered is far below that needed to satisfy the sludge flow con-
straint. Of relevance is the high angle case, where theory and
experiments have been used to define the dependence of the critical
flow rate for the onset of turbulence at the interface (i.e. Qturb)
on the settler angle, the channel spacing and the density difference
between the clear liquid layer and the feed suspension layer.
A number of significant findings have been made which should serve
as a useful basis for the design of a stably operating system:
i) that the difference in specific densities between the clear
l.iquid and feed suspension layers, lI~g, leads to a gravitational
instability. The longitudinal component of the densimetric
gravitational acceleration 0>J1.COSD(., which is the driving p
force for the buoyancy flow, is the chief cause of instability;
81
while the transverse component ~ sinn is stabilising. It p
therefore suggests that the critical flow rate for the onset
of turbulence, Qturb' is proportional to Cotn.
ii) that based on linear analysis,
Qturb is proportional to (~)-!
which r~inforces the argument that the densimetric gravitational
acceleration on the whole has a destabilising influence, and
iii) that Qturb is proportional to b~. i.e. a wider channel has a
higher settler efficiency. However, it is found that a limiting
value of Qturb is reached for b larger than 10 cm. The reason
being that above about 10 cm the upper channel wall is so far
away from the fluid interface that so far as the interface
is concerned, it can be considered to be at infinity.
Whilst the proportionality relationships above are capable of
providing some design guidelines for achieving flow stability, they·
are by no means complete, and hence cannot as yet be used directly
in design calculations to provide the desired settler dimensions.
An important omission is the settler length, which must have a
significant effect on the wave formation at the interface.
This part of the research programme is therefore aimed at
establishing the effect of settler length on flow instability in
order to supplement the existing theory. Based on the wave theory
A?
it follows that excessively long and narrow channels will be
susceptible to flow instabilities because any wave disturbance
that is generated along the length of the interface will have a
chance to propagate and amplify to breaking point, whence particles
get ejected into the clear liquid stream. It is believed that, for
a given channel spacing and angle of inclination, there exists a
corresponding optimum channel length beyond which negligibly small
improvement 'to the settler efficiency can be .expected. It is
planned to verify experimentally the existence of such an optimum
channel length and to recommend its use as an upper limit for the
purposes of design.
4.2.4 Sludge Flow Constraint
In this section mainly proposals will be made for establishing
the requirement of the sludge flow constraint which must be satis
fied in order to achieve an effective removal of the sludge collec
ted on the lamella plates.
Though it is obvious that the provided angle of inclination (a)
should be sufficiently large to cause an effective flow, such an
angle is in practice not easily defined because of the lack of
understanding of the sludge flow behaviour. It is evident from
the 1 it~raturethat this area of research has been severely neglected
and no known attempt to describe the sludge flow behaviour, either
qualitatively and quantitatively, has ever been made.
83
The normal practice of overproviding the angle. of inclination
is undesirable because of the competing interest to obtain the
greatest projected area for sedimentation. The underprovision of
a, on the other hand, is even more undesirable because it will
result in poor sludge flow leading to a build-up along the entire
length of the lamella plates. In extreme cases the sludge layer
may grow eventually to fill the entire channel, thereby rendering
the separator inoperable.
As an attempt to remedy this problem, an experimental invest
gation is planned with the aim to establish the following objec
tives:
i) to establish the mechanisms of sludge flow and to determine
some of the relevant parameters in order to devise the means
of enhancing the flowability of the sludge layer,
ii) to determine the effects of the different flow patterns (i .e.
cocurrent and countercurrent flows) on the efficiency of
sludge removal in a continuous system, and
iii) to verify the existence of an optimum angle of inclination.
It is believed that such an optimum exists, i.e. that which
is capable of providing the desired level of sludge thickening
at the maximum separator throughput.
Having achieved these objectives it will then be possible to
offer some useful and reliable design guidelines for effective sludge
thickening to be appl i ed to a real continuous system.
84
4.3 SIZING METHOD
A significant outcome of the theoretical development by Hill
is that the rate of sedimentation in an inclined vessel can be
accurately predicted with the use of the Nakamura and Kuroda equa
tion, provided that A is asymptotically large (i.e. A + 00). The
latter has since been ratified theoretically and experimentally by
Acrivos and Herbolzheimer. Based on batch inclined settling tests,
the authors have been reported to obtain excellent agreement between
the experiments and the theoretical predictions. It is our intention
to extend the application of the Nakamura and Kuroda equation to
predict the operating capacity of a continuous lamella separator.
It is believed that good predictions can be achieved because, for
most practical interests, A is generally large, i.e. 0(105) or
greater. .
A general equation* for predicting the overall capacity of a
lamella separator will be described below. Consider a continuous
separator with feed rate Qf at solids concentration co' that is.
used to produce a particle-free overflow (i.e. supernatant) Qo'
and an underflow, Qu' with solids concentration cu' From the
overall material balance and solids balance, the feed rate (i.e.
the overall separator capacity) can be expressed in terms of the
overflow rate as:
* Applicable to all the different modes of operation: Cocurrent, countercurrent or middle-feeding.
85
· . CO""",;;~---- --
Underf10w: Q c u' u
" ,
verflow:
/,feed :
Qo Qf' Co (cocurrent)
'Middle-feeding
Eqn. 4.23
Substituting Qo with the Nakamura and Kuroda equation, the feed
rate can now be expressed in terms of the separator dimensions and
the suspension properties as:
Q = f
b v W h S' o (1 + 1n8) Cose b
(1 _ CO) Cu
bvoW hS' h Q (1 + b 1ne) were 0 = Cose
(the Nakamura and Kuroda equation).
RI'>
Eqn. 4.24(a)
Eqn. 4.24(b)
Since, in most industrial applications, the ratio of the vertical
height of the separator to the channel spacing (h/b) is much
greater than 1, Equation (4.24) may be simplified to:
i.e.
bvoW h S· ( ln9)
Q = -"-Co,,-,s;..,;s'----,.,;... . ..;,.b_ f (1 _Co)
Cu
h v W tans Q = _-=.0--r:--f (1 _ CO)
Cu
Replacing the vertical height of the separator, h, by its actual
length, x, the predictive equation in its final form becomes
x vo WSins
(1 _ CO) cLi
Eqn. 4.25
In accordance with the Nakamura and Kuroda's theory, Equations
(4.24) and (4.25) are expected to work well only under the following
set of conditions:
• laminar flow
• small particle Reynolds number, and
• large. A
However, the approximate range of A over which the above equation
can be expected to apply well will have to be determined experimentally.
87
4.4 PROPOSED DESIGN SCHEME
Most existing design methods for lamella separators are deve
loped using the assumptions of ideal settling conditions. However,
because the requirements for achieving such ideal conditions are
often not sufficiently met by the design, non-idealities do occur.
To account for the latter, correction factors are subsequently
used. Non-ideal conditions in practice include those arising from
poor sludge flow along the lower incline'd surfaces and flow insta
bility,to name but a few. A cause for great concern is that because
the correction factors are generally arbitrary in nature, they tend
to be excessively large. As a consequence, the end result is usually
one of an uneconomic design .that is far below the optimum.
In the light of recent research findings regarding flow
stability and steady-state conditions in the settling channel, it
is becoming apparent that substantial improvement to the existing
design methods can now be made. As a step in that direction, a
design scheme is proposed in which constraints are imposed on the
relevant design variables in order to suppress the various potential
causes of non-idealities. A summary of the various so called "ideal
state" constraints and the design variables they influence - both of
which have already been established in Section 4.2 - are listed in
Table 4.1 overleaf.
88
TABLE 4.1: SUM~'ARY OF DESIGN VARIABLES AND CONSTRAINTS
Design Constraint
Sludge flow
Physical (clogging)
Steady-state
Flow stabi li ty
Lami nar fl ow
Design Variable(s)
Angle of inclination
Channel spacing
Angle of inclination Channel spacing channe 1 1 ength
Angle of inclination Channel spacing Channel 1 ength
Channel spacing Channel width
It is evident from the table that some of the design variables
may be subjected to the influence of more than one constraint, for
example, the angle of inclination will be influenced simultaneously
by the sludge flow, steady-state and flow stability constraints.
In such a case, however, the sludge flow constraint which is most
dependent on the angle of inclination will have the overriding
influence. The use of such constraints on the design variables in
the proposed scheme to design a lamella separator is described
below.
The advantage of a lamella separator arising from the enhanced
rate of sedimentation will be short-lived if the corresponding
increase in the quantity of solids collected on the lower inclined
surfaces is not as rapidly discharged. In extreme cases this
deficiency may lead to partial clogging of the settling channel.
It is therefore vital that the inclination angle of the separator
89
be sufficiently steep to satisfy the first constraint of the proposed
design scheme, i.e. the sludge flow constraint. The latter is a
safeguard for achieving a continual and rapid removal of sludge
collected on the lower inclined surfaces.
Having provided a suitable angle of inclination to avert the
build-up of a sludge layer along the length of the lamella plates,
it is equally important that a physical constraint be imposed on the
channel spacing to ensure that the shear bulk of the sludge being
discharged fron the base of the lamella plates does not create
clogging problems. As a rule of thumb a typical channel spacing
of about 5 to 10 cm is used depending on the types of suspension
being treated. The upper value is usually used in the treatment
of industrial waste sludges because of their greater potential
clogging problems.
Though the channel spacing is also under the influence of
both the steady-state and flow stability constraints (as shown in
Table 4.1), the physical constraint is considered to have the over
riding influence because .it is most dependent on the channel spacing.
The burden to satisfy the steady-state and flow stability constraints
is now transferred to the channel length. It is already established
in Section (4.2) that for a·given angle of inclination and channel
spacing there exists a corresponding limiting channel length within
which the formation of steady-state stratified layers is possible.
It is therefore cruci a 1 that the desi gned channel length is always
less than the limiting value. In addition, the flow stability
constraint also has a limit on the channel length in order to
90
minimise the re-entrainment of particles into the clear liquid
stream. In the final analysis it is proposed that the designed
channel length be based on the more limiting of the two constraints.
Having specified the angle of inclination, the channel spacing
and the channel length, the 1aminar flow constraint is then applied
to give the required channel width. The latter should be such that
the resulting hydraulic diameter gives a Reyno1ds number of no
greater than 500. To complete the design, the required number of
channels is then specified.
By taking steps to prevent the creation of non-ideal conditions
in this way, it is expected that substantial improvement to the
overall design can be achieved. A diagrammatic presentation of the
design steps as proposed in the scheme is shown in Figure 4.5.
91
FIGURE 4.5: PROPOSED DESIGN SCHEME FOR LAMELLA SEPARATORS
Design Specifications
Sludge flow constraint
( ANGLE OF INCLINATION .. , ~
Physical constraint (i.e. potential clogging)
CHANNEL SPACING --------Steady-state Flow stability constraint constraint
( CHANNEL LENGTH )
Laminar flow constraint ..
( CHANNEL WIDTH )
Number of settling channels required
92
CHAPTER 5
EXPERIMENTAL'PROGRAMME
5.1 INTRODUCTION
5.2 EXPERIMENTAL VERIFICATION OF INCLINED SEDIMENTATION BEHAVIOUR ... 5.2.1 Test materials ...
5.2.1.1 Criteria fOr choice of materials 5.2;1.2 Details of particles 5.2.1.3 Details of suspension liquid
medium 5.2.2 Batch settling tests .. ,
5.2.2.1 Design and construction of set-t1 ing vessel; ..
5.2.2.2 Photographic analysis ... 5.2.2.2.1 Experimental procedure 5.2.2.2.2 Technique for producing
slit of laser light 5.2.2.3 Liquid velocity measurements 5.2.2.4 Agitator 5.2.2.5 Prevention of ,air bubbles 5.2.2.6 Constant temperature control
5.2.3 Continuous settling tests 5;2.3.2 Design and construction of lamella
separator ... 5.2.3.2 Continuous flow arrangement 5;2.3.3 Experimenta 1 procedure ' ...
5.3' STUDY OF BEHAVIOUR OF SLUDGE FLOW ALONG THE LOWER
Page No 94
97
97 97 98
99 100
100 101 101
103 104 112 113 114
114
114 117 119
INCLINED SURFACE 121
5.3.1 5.3.2 5.3.3
Test materials Experimental equipment' Experimental procedure
93
121 123 125
5.1 INTRODUCTION
CHAPTER 5
EXPERIMENTAL PROGRAMME
The principal objective of this experimental programme is to
verify the theoretical predictions of inclined sedimentation beha
viour in both batch and continuous systems. The analysis of batch
inclined sedimentation behaviour is included in the programme
because it is capable of providing useful guidelines for the
continuous operation.
In a series of batch inclined sedimentation experiments a cine
photographic technique was used to verify the predicted profile of
the clear liquid layer formed beneath the upper inclined surface.
Using a system of particles and liquid with closely matched refrac
tive indices and with side illumination from a laser source, it was
possible to analyse accurately the entire settling process from
start to finish. The predicted velocity field in the clear liquid
layer was also verified experimentally in a separate series of expe
riments. A laser dopp1er anemometer was used for that purpose. The
latter had the advantages that there was no obstruction to the actual
liquid flow and its high spatial resolution (typically 20-100 ~m) far
exceeded that obtainable by other methods. All the experiments were
conducted in parallel sided vessels under the following sets of con
ditions:
94
aspect ratio of vessel (i.e. h/b) = 0(1) - 0(100)
concentration of solids in suspension = 0-30 volume %
angle of inclination = 0_900.
In a series of continuous inclined sedimentation experiments
the maximum overflow rates of pure particle-free supernatant were
obtained and subsequently compared with the theoretical predictions.
The following sets of experimental conditions were covered:
aspect ratio of continuous separator = 0(1) - 0(100)
channel spacing = 1.5 - 3.4 cm
concentration of solids in suspension = 0.5-2 volume %
angle of inclination = 0_900.
Cocurrent and countercurrent flows were tested and the former included
both the subcritical and supercritical modes of operation. The exis
tence of two optimum operating conditions were also verified experi
mentally: i.e. the optimum aspect ratio and the optimum angle of
inclination. In practice, the former would impose an upper limit
on the length of the separator to ensure minimal re-entrainment of
particles into the supernatant. On the other hand, the optimum
angle of inclination would give a continual and rapid removal of
sludge along the lower inclined surface of the lamella separator.
Also included in the experimental programme were exploratory
experiments to study, in particular, the mechanisms and parameters
governing the sludge flow behaviour on the lower inclined surface.
95
A specially constructed batch rig was used for this purpose.
Results from this series of experiments will be used to devise a·
design strategy for achieving maximum separator throughput with
high sludge concentration in the underflow.
The remaining part of this chapter is devoted to describing
the details of the experimental facilities i.e.
. .. , test materials used in the experiments and their selection
criteria;
details of the experimental rigs;
details of the experimental techniques and operating proce
dures.
96
5.2 EXPERIMENTAL VERIFICATION OF INCLINED SEDIMENTATION BEHAVIOUR
5.2.1 Test Materials
5.2.1.1. Criteria for choice of materials
The choice of test materials is governed principally by the
need to match closely the refractive index of the particles to the
suspension liquid medium. This is a prerequisite of the laser
photographic technique that is developed for analysing the settling
behaviour of suspensions in inclined vessels. Details of this tech
nique are given in Section 5.2.2.2.
To simulate the settling conditions that are typical of most
industrial applications, i.e. having both low sedimentation and
particle Reynolds numbers, a fairly viscous suspension liquid and
small particles are needed. Moreover, to keep the fluid mechanics
simple requires the particles to be spherical and the suspension
liquid to be Newtonian in nature.
Based on these criteria the following closely matched refractive
index system has been developed for the purposes of our experiments.
97
TABLE 5.1 : CLOSELY MATCHED REFRACTIVE INDEX SYSTErl
Particles
Type:
Si ze range:
Specific gravity:
Colour:
Refractive index:
Sedimenting liquid medium
Composition:
Specific gravity:
Viscosity:
Refractive index:
Spherical soda glass beads
90-125 l.lm
2.46
Clear
1.510
74.5 volume % Reomol DBP) CIBA-GEIGY 25.5 volume % Reofos 65) plasticisers
1.0795
22.2528 centipoises @ 250C Newtonian in nature
5.2.1.2 Details of particles
The glass beads used in the experiments were between 90 to 125 l.lm
being the sieved and retained glass beads from original samples of
between 63-150 l.lm. Preliminary tests confirmed that this size range
was sufficiently narrow to prevent any significant effect of size
segregation within the suspension. This was also partly because
all the experiments were conducted under hindered settling conditions.
98
Non-spherical glass beads were removed from the bulk sample
with the use of a vibrating inclined surface (i.e. inclined at
approximately 10 degrees from the horizontal). The spherical
glass beads, by virtue of their higher freedom of rotation, rolled
rapidly to the bottom of the inclined surface where they were collec
ted. However, the non-spherical ones remained along the inclined
surface and were subsequently removed.
, .. A common specific gravity for the remaining glass beads was
obtained by removing the imperfect ones, i.e. those with voids in
them. This was easily achieved by floating the imperfect beads in
a mixture of Carbon Tetrachloride and di-iodomethane having the same
specific gravity (i.e. 2.46) as the perfect glass beads. The compo
sition of that liquid mixture is given below:
Carbon Tetrachloride (5g = 1.595)
di-iodomethane (5g = 3.135)
43.83 weight %
56.17 weight %
Because of the extensive use of glass beads and the difficulty
in preparing them the used ones were recycled whenever possible.
5.2.1.3 Details of the suspension liquid medium
Two plasticisers were mixed in the following proportions to
produce a suspension 1 i qui d medium with a refractive index of 1. 511,
which closely matched that of the soda glass beads (R.I. = 1.510):
Reomol DBP
Reofos 65
74.5 volume %
25.5 vo1 ume %
99
The rheological properties of this plasticisers mixture were
obtained with the use of a Weissenberg R18 Rheogoniometer. The
mixture was confirmed to be Ne\~tonian in nature and having a
viscosity of 22.2528centipoises at 250C - the temperature at
which all the experiments were conducted.
5.2.2 Batch Settling Tests
5.2.2.1 Design and construction of settl ing vessel··
The batch settling tests were carried out in rectangular and
square cross-section vessels set on their edges. Both low and high
aspect ratio vessels were used and their dimensions, as indicated
in the diagram, are given below:
Ty'pe of Vessel
Low aspect ratio
High aspect ratio
Length (L), cm
25
115
100
Height (b), cm
5
1.16
Width (w), cm
5
5
For photographic reasons the vessels were constructed entirely out
of transparent clear perspex.
5.2.2.2 Photographic analysis
A set of experiments was carried out to verify the theoretical
predictions of the clear liquid layer formation using photographic
analysis - the details of which will be given below. The tests were • conducted in both low and high aspect ratio vessels and at particle
concentrations ranging from 1 to 30 percent by volume.
5.2.2.2.1 Experimental procedure
The batch settling vessel was foremost positioned on its edge
and set at the desired angle of inclination. The required quantities
of glass beads and the suspension liquid mixture were then introduced
into the vessel to make up the desired concentration of suspension.
A narrow slit of laser light was focused on the side of the
ve sse 1 to ill umi na te the sus pens i on with in - see Fi gure 5.1. (The
method by which this narrow slit of laser light is produced is dis
cussed in Section 5.2.2.2). A cine-camera was then positioned normal
to the front surface of the inc1 ined vessel in readiness to film the·
entire settling process.
Strong agitation was applied initially to remove any trapped
air from the glass beads in the suspension. An agitator in the form
of a perforated plate was used for this purpose. Being free of air,
the suspension was once again agitated until homogeneity was achieved.
101
~
o N
15 mW He-Cd laser Concave lens
Convex lens
Cyl indri ca 1 lens
FIGURE 5.1: EXPERIMENTAL ARRANGEMENT FOR LASER-PHOTOGRAPHIC ANALYSIS
Inclined
[""
/
Gentle agitation was applied to minimise any residual disturbance
that might be induced by the agitator. Immediately after the
cessation of agitation, the agitator was removed completely from
the suspension and the entire settling process was filmed from
start to finish. Zero experimental time was defined as the moment
--that agitation ceased.
Experimental ·data for the thickness of the clear liquid layer
formed in the settling vessel was then obtained from the films via
a Vanguard machine. The latter is essentially a sophisticated form
of projector that allows a frame by frame analysis of the cine-fi1ms
to be carried out. In addition, the rate of generation of clear
liquid and the behaviour of particles in the settling channel were
also analysed. These experimental results were subsequently compared
with theoretical predictions.
5.2.2.2.2 Technique for producing slit of laser light
A novel technique was developed for producing a narrow slit of
laser light (approximately i mm in width) to illuminate a given region
in the settling suspension so that the entire settling process could
be filmed using a cine-camera.
The experimental arrangement that was devised for this purpose
is show·n in Fi gure 5.1. A sufficiently long and narrow sl it of
light was produced from a fine and originally circular laser beam
(from a 15 mW Helium-Cadmium source) with the use of a cylindrical
lens. The length of the slit was controlled by a concave lens,
103
which was used to magnify the initial laser beam. Moreover, to
improve the sharpness and intensity of the slit a convex lens was
used to concentrate the magnified laser beam (from the concave
lens) onto the cylindrical lens. The He-Cd laser tube and the
set of lenses were all secured to an optical bench and the latter
was bolted to a stand, which allowed the whole laser unit to be
moved vertically along its main rod. In this way the entire length
of the settling vessel could be illuminated for filming purposes.
5.2.2.3 Liquid velocity measurements
A series of experiments was conducted to verify the predicted ,
velocity fields in the clear liquid layer that was formed during
batch inclined sedimentation in low aspect ratio vessels. The
liquid velocity measurements were made using a Malvern Laser Doppler
Anemometer. The principle of the measurement technique was to detect
the Doppler shift in two convergent laser beams caused by microscopic
dust particles suspended naturally in the liquid stream. The Doppler
shift was then analysed in a signal processor to produce an average
time for the dust particles to pass from one fringe to the next of
the interference pattern set up by two intersecting laser beams
(see Figure 5.2). Since the distance between fringes was known,
the liquid velocity was easily ~alculated.
As.shown in Figure 5.2, the apparatus used consisted of a
15 roW Helium-Cadmium laser fitted with a phase modulator and a
beam splitter. The latter was used to split the original beam into
104
two beams of equal intensity which were then combined to produce a
fringe system at the cross-over point. With the use of a drive
unit on the phase modulator the fringes were caused to move
linearly in space either in the same direction as the flow, or
against the flow. The result being to decrease or increase the
Doppler shift detected by the signal processor so that the direc
tion of flow could be ascertained.
15mW He-Cd Laser
Si gna 1 Processor
Phase Modulator Drive Unit
1fVV\1 Oscill os cope
Display
Photomultiplier Detection System
Optical fringes ~ ~ which are nor- ~T mally stationary are caused to move with, or against, the flow to resolve it actual direct;
~--
Flow stream Beam Phase splitter modulator
FIGURE 5.2: ARRANGEMENT OF MALVERN LASER ANEMOMETER OPERATING IN FORWARD SCATTER MODE
105
FIGURE S.3(a): SIGNAL PROCESSOR OF LASER ANEMOMETER
/
FIGURE S. 3(b): EXPERU'!ENTAL ARRAtliEfoENT fOR LIQUID VELOCITY MEASUREMENTS
106
A photomultiplier was positioned in front of the cross-over point
to detect the Doppler shift frequencies, which were in the form
of photon signals. Analog pulses of these photon signals were
counted and then stored in digital form in a Malvern K7023 digital
correlator. Output from the signal processor was obtained either
in graphical form on an oscilloscope, or in numerical form on a
computer printout. A photographic view of the experimental arrange
ment is shown in Figures 5.3(a) and 5.3(b).
Experimental procedure
The first step in the experimental procedure was to create a
homogeneous suspension using the same method adopted for the clear
liquid layer measurements as described in Section 5.2.2.2.1. The
suspension was then allowed to settle until steady-state condition
was reached before any velocity measurements were made. The time
taken to reach steady state was determined in an earlier experiment,
and under the same settling conditions. Liquid velocity measurements
were made at pre-selected pOints along the thickness of the clear
liquid layer and over the length of the vessel along the centreline
of its width - see figures overleaf. This centreline was
chosen out of convenience, since the settling behaviour was
essentially 2-dimensional in nature and independent of the width
of the vessel. The measured liquid velocities were then resolved
in the direction normal to the clear liquid layer thickness to
give the desired longitudinal components, u. The latter were
107
0D ~ clear liquid layer thickness
u ~ longitudinal velocity component
. :
,-_..::::;'------Clear liquid layer
Suspensi on 1 ayer
/ ____ -{-______ Steady state clear liquid layer profile
subsequently compared with the theoretical predictions. Through
out experimentation the laser, photomultiplier and digital corre
lator were left on except for the digital counter, which had to be
manually switched on whenever any measurements were made.
108
Operation of the digital counter gave a trace on the oscilloscope
screen of the type shown in Figure 5.4, from which the values of
91' g2 and g3 were obtained.
G2 1-- ... : . . . . . . . : '. · · . · ' . . . . . . . . . . . . . . . . . . · . . . · . . ·
1 . . ..
.
r g2
g3 g,
FIGURE 5.4: TYPICAL OSCILLOSCOPE TRACE FROM LASER DOPPLER ANEMOMETER
This was done by switching the digital output control to the
channels corresponding to gl' g2 and g3 respectively.
The longitudinal component of the measured liquid velocity, u,
was calculated using the standard equation below:
109
u ={(samp1e time per c } Eqn.5.1
where Cl = angle between the fringes and the direction of the longi
tudinal velocity component.
(In our experiments this angle was set equal to the angle of incli
nation of the vessel, measured from the horizontal).
The denominator on the right-hand side of Equation 5.1 is the machine
formula for calculating the average time between fringe interference.
The sample time per channel was a pre-set value and the channel number
of the 1st peak was given by G2 on the oscilloscope trace. The fringe
spacing, s, was calculated using the following equation:
i S = d
A \lR
where: A = wavelength of the He-Cd laser beam (= 0.4416 \lm)
Eqn.5.2
\lR = refractive index of the sllspension liquid (= 1.511)
i and d = functions of beam divergence and were obtained by
projecting the laser beams onto a wall a fair distance
away.
i ---1 --::::~~=---__ -"lT
----.J~
110
In addition, the turbulence intensity, n, at the position of measure
ment was estimated using the equation below:
i.e.
where:
(r-l) +--.L 2N2
N = number of fringes in rms beam radius.
Eqn.5.3
However, in all our experiments the turbulence intensity was negl i
gibly small, with r being practically 1 and tl, greater than 20.
Hence the measured liquid velocity calculated via Equation 5.1 was
taken to represent the true velocity without any necessary correction
for turbul ence. A typi ca 1 oscilloscope trace obtained in our experi
ments is shown in Figure 5.5.
FIGURE 5.5: TYPICAL OSCILLOSCOPE TRACE FROM PRESENT EXPERIMENTS SHOWING NEGLIGIBLE TURBULENCE
III
5.2.2.4 Agitator
Figure 5.6 shows the agitator used to create a homogeneous
suspension in the batch settling vessel. It is made up of a
circular cross-section rod welded at the bottom end to a square
perforated plate with a set of five equally spaced holes.
Base: ----{ plate
Equally spaced holes
FIGURE 5.6: AGITATOR FOR BATCH SETTLER
The size of the base plate is made just slightly smaller than the
internal dimensions of the batch vessel to promote effective dis
persion of particles in the suspension.
11?
Agitation of the suspension was provided by a cyclic up and
down movement of the perforated plate along the length of the
inclined vessel. For consistency, the number of cyclic movements
of the agitator was fixed at 20 in every test. Preliminary tests
showed that any residual disturbance in the suspension that was
induced by the agitator was small and rapidly dissipated, i.e. less
than 5 seconds after the cessation of agitation. Thus it would
have a negligible effect on the actual behaviour of the settling
suspension. The rapid dissipation was brought about by the viscous
suspension liquid which provided a strong damping effect.
5.2.2.5 Prevention of air bubbles
When using the agitator care was taken to prevent the introduc
tion ·of air bubbles into the suspension. During the cyc1.ic movement
of the agitator its perforated plate was always kept within the
bulk suspension so that it could not generate air bubbles through
surface breakages at the liquid/air interface. The introduction of
air bubbles into the suspension was prevented because of the follo
wing potential problems:
i) the rising air bubbles could disturb significantly the actual
settling behaviour of the suspension, thus producing erroneous
experimental results.
ii) on film the actual settling particles might not be distingui
shable from the air bubbles because they both appear as traces
of dark dots. Consequently, accurate analysis of particle
113
motion on the Vanguard would be very difficult, if not,
impossible.
iii) measurements of liquid velocities using the Laser Doppler tech
nique relied on the presence of microscopic seeding particles
in the liquid stream - details already given in Section 5.2.2.3.
The presence of air bubbles, which are generally much larger,
might themselves act as seeding particles and could introduce
errors into the velocity measurements.
5.2.2.6 Constant temperature control
To eliminate any thermal effects in the settling suspension all
the experiments were conducted in a constant temperature room main
tained at 25 0C ± 0.20 C.
5.2.3 Continuous Settling Tests
5.2.3.1 Design and construction of lamella separator
The continuous settling tests were performed in the lamella sep
arator shown in Figure 5.7. It was constructed from transparent clear
perspex and consisted essentially of a main separator body, a sludge
collector and a clear liquid removal chamber.
The entire separator was designed in modular form so that a
wide range of settling channel aspect ratios (0-75) could be obtained
with a channel spacing of 1.5-3.4 cm and at an inclination angle of
0-900 . The internal dimensions of the rectangular modules that
formed the main body of the separator are given overleaf:
114
. .
No. of rectangular Internal dimensions of module modules available Length, Width, Channel Spacing
cm cm cm
1 17 4 3.4
2 46 4 3.4
Each of the rectangular modules was designed so that a perspex
spacer plate may be inserted to divide it into two compartments of
equal dimensions. In this way the channel spacing could be varied
from 3.4 cm to 1.5 cm.
By using different modules for the feed section the separator
could be adapted to operate in both cocurrent and countercurrent
flows. Moreover, in the cocurrent flow, both subcritical and super
critical modes could be achieved. In the cocurrent operation the
feed was introduced at the top of the settling channel through an
inlet whose thickness could be varied by an adjustable perspex plate.
The thickness of the feed layer could be adjusted to less than or
greater than about half the channel spacing according to whether the
supercritical or subcritical mode of operation was required. On the
other hand, in the countercurrent operation the feed was introduced
near the bottom of the separator in such a manner as not to disturb
the solids already settled on the lower inclined surface.
"~
. .
LaJrella separator
FIGURE 5.7: EXPERIMENTAL RIG FOR CONTINUOUS LAMELLA SEPARATOR
116
A magnetic stirrer was installed in the sludge collector to
facilitate the removal of solids in the underf10w stream. The
entire separator was supported between two rigid stands and could
be positioned at any angle between the vertical and the horizontal.
5.2.3.2 Continuous flow arrangement
Figure 5.8 shows diagrammatically the flow arrangement used in
the continuous inclined sedimentation experiments. A feed tank was
provided in which a homogeneous suspension was created using a
blade-paddle stirrer. The latter was sufficiently powerful to
remix the suspension even after all the particles had settled out.
The temperature in the feed tank was controlled at 250C ± O.loC by
a thermostatically controlled heater used in conjunction with a
cooler.
In a normal operation the feed was introduced into the separator
and the overflow and underflow were recycled to the feed tank. The
underf10w was pumped back to the feed tank by a perista1tic pump
(Heido1ph type SP) whose capacity (maximum 1 litre per minute) could
be regulated by adjusting its pump speed and using a tubing of
appropriate size. The overflow, on the other hand, was recycled
by a small centrifugal pump. The flow rate of this stream was
regulated by valve V4 and measured with an in-line rotameter.
The turbidity of the overflow was measured by a Hach Turbidimeter,
which covered a range of 0-100 NTU. Sample points SPl, SP2 and SP3
were provided for determining the solids concentration in the feed,
overflow and underf10w streams respectively.
117
Blade-paddle stirrer Thermostatical y controlled ~_-!-~~===cooler heater r-
Rotameter
vs
r-~ t
SP2 I
SP3
Hach-Turbidimeter (off-l i ne)
Peristaltic p~p (P2)
FIGURE 5.3: CONTINUOUS FLOW ARRANGEMENT
118
Feed tank
,." .
5.2.3.3 Experimental procedure
A general experimental procedure for the continuous operation
is summarised as follows. Initially the feed tank was filled with
the suspension liquid. The lamella separator was positioned at
the desired angle of inclination and feed lines were connected to
the appropriate inlets chosen for the experiment. Valves Vl-V5
were then opened to fill the whole system. Following that, Vl and
V4 were closed and the feed tank was topped up with more sus~en
sion liquid. The required quantity of glass beads was then added to
make up the desired concentration of suspension. The total volume
of suspension in the feed tank was about 10 litres. The blade
paddle stirrer was switched on for a brief period to provide some
initial agitation to liberate trapped air from the sample of glass
beads. After the air bubbles had been removed the stirrer was again
switched on, but at a higher speed, to create a homogeneous suspen
sion. The constant temperature controller in the feed tank and the
magnetic stirrer in the sludge collector were also switched on.
Valve Vl was then opened and the centrifugal pump, Pl, was switched
on to recycle the overflow to the feed tank. The overflow was con
trolled with V4, which was gradually opened until the desired flow
rate was obtained. The latter was taken as the point at which solids
first appeared in the overflow, and represented the maximum over
flow capacity of the separator. The presence of solids was detec
tedbya sudden increase in the turbidity of the overflow which was
measured with a Hach-Turbi.dimeter. The peristaltic pump, P2, was then
switched on and the pump speed was adjusted until a ratio of 1 to 3
119
in the underf10w to the overflow was achieved. The same ratio was
maintained in all the continuous experiments to provide a basis
for comparison of separator performances.
The operation was then kept running for about 1~-2 hours. At
intervals of 10-20 minutes, samples were obtained from SP1, SP2 and
SP3 to determine the solids content in the feed, overflow and under
flow streams respectively. Material balances based on the solids
were then made to determine the attainment of steady-state condi
tions, i.e. when" the sol ids fluxes into and out of the separator
were balanced. In most of our experiments steady-state was reached
after about 1 hour. However, in cases where the angle of inclina
tion of the separator was insufficiently large (i.e. approximately
200 from the horizontal), it was impossible to attain steady-state
condition because of the transient behaviour of sludge flow along
the lower inclined surface.
120
.....
5.3 STUDY OF BEHAVIOUR OF SLUDGE FLOW ALONG THE LOWER INCLINED SURFACE
The sludge flow behaviour of several fully dispersed solidi
liquid systems were examined. both qualitatively and quantitatively.
in a specially constructed batch rig. The objectives were to esta
blish the sludge transport mechanisms and their dependence on the
angle of inclination .
5.3.1 Test Materials
Details of the different fully dispersed systems used in the
experiments are listed in Table 5.2.
Type of Dispersed System Nature of Solids
Liquid So 1 i ds Size Range Speci fi c Shape (llm) Gravity
Di sti 11 ed Glass beads 90-125 2.46 Spherical water
" Glass beads 355-420 2.46 Spheri cal
" Bmnz"- S\'''e"".,. 90-125 7.70 Spheri cal
" Powdered 90-125 2.21 Irregular. angular glass fragments
" Limestone 90-125 2.74 Irregular. granu-lar
" Zircon 90-125 4.22 Irregular. granu-lar
Reofos 651 I Glass beads 90-125 2.46 I Spheri ca 1 Reomol DBP
TABLE 5.2: THE DIFFERENT FULLY DISPERSED SYSTEMS USED IN THE SLUDGE FLOW EXPERIMENTS
121
(a) Soda glass beads .(90-125 m)
(c) Bronze spheres
(e) Zircon
(b) Soda glass beads (355-420 m)
(d) Limestone
(f) Powdered glass
FIGURE 5.9: MICROGRAPHS OF SOLIDS USED IN THE DIFFERENT FULLY DISPERSEDSYSTEt1S
122
o
• •
0"
, .
.-. o • • 'e "e.
••
The solids listed above were all incompressible by nature and
were narrowly sized using standard sieves. The first set of dis
persed systems, i.e. those using distilled water, was designed to
study the following parameters which were postulated to have sig
nificant effects on the sludge flow behaviour:
i) Shape and surface texture of solids (see micrographs in
Figure 5.9) •.
il) Density difference between the solids and liquid, and
iii) Size of solids.
Water was predominantly used because of its relevance to most indus
trial applications. However, to study the effects of liquid viscosity
another dispersed system was developed in which plasticisers mixture
(i.e. the refractive index matching liquid) was. used. The latter
was chosen because it was also used in the continuous system and,
hence, both sets of experimental results could be directly inter
related.
5.3.2 Experimental Equipment
The sludge flow experiments were carried out in a rectangular
vessel of internal dimensions 5 cm x 5 cm x 50 cm. It was construc
ted entirely out of transparent perspex to enable visual examination
of the sludge transport behaviour (see Figures 5.10(a) and 5.l0(b)).
The upper top surface of the vessel was left opened for the test
materials to be added. The vessel was mounted on an optical stand,
which provided the capability of varying the angle of inclination
123
le}
Optica 1 _____ _ stand
(b)
Stirrer
opper-----
---Fine adjustment rod
-----Vessel
----Plum-line
---Fine423.d,j ustment rod
FIGURE 5.10: EXPERH1ENTAL RIG FOR THE STUDY OF SLUDGE FLOW BEHAVIOU~ . 124
· .
from 0 to 90 degrees. In addition, a fine control on the increment
to the angle of inclination was provided in the form of a fine
adjustment rod, as shown in Figure 5.l0(b). A contraption consisting
of a pl umb-l ine and a protractor was 'used to measure the angle of
inclination. A stirrer was used in conjunction with a stopper to
create a homogeneous suspension from which a uniform layer of
sludge was formed along the length of the lower inclined surface,
except for a short distance of about 10 cm from its base. The
latter provided a free surface for sludge flow.
5.3.3 'Experimental Procedure
A summary of the steps in which the experiments were conducted
is listed below:
i) The vessel was first filled with the desired quantity of
1 iquid.
i i) The stopper was then positi oned at the 10 cm mark (denoted by
"A" in Figure 5.l0(a.)) in the vessel before the required quantity
of solids was introduced.
iii) Using the stirrer the entire mixture was agitated to produce
a homogeneous suspension.
iv) The solids in the suspension were then allowed to settle to
form a sludge layer on the lower inclined surface. With prac
tice and care it was possible to produce an even layer of sludge
over its entire length.
l?<:
v) The stopper and the stirrer were then shifted to the bottom
end of the vessel to leave a free surface for sludge flow
(represented by the shaded area in Figure 5.l0(a)).
vi) The vessel was then gradually but gently inclined until sludge
movement first occurred. The nature of the sludge movement
and the angle at which it occurred were recorded in detail.
vii) After the initial sludge movement had ceased, step (vi) was
repeated until the entire sludge layer was removed.
viii) For every experimental run the entire procedure listed above
was repeated for at least half-a-dozen times to obtain accep
table average results.
All the experiments were conducted in a constant temperatur~
room maintained at 250C ± O.2oC.
l~
6.1
CHAPTER 6
DISCUSSION OF RESULTS
EXPERIMENTAL VERIFICATION OF BATCH INCLINED SEDIMENTATION MODELS ... 6.1.1 Inclined Sedimentation Models of Acrivos
and Herbolzheimer
6.1.1.1 Low aspect ratio case
6.1.1.1.1 Steady-state clear liquid/ suspension interface
6.1.1.1.2 Velocity field in the clear liquid layer
6.1.1.2 High aspect ratio case
6.1.2 Experimental Verification of the Nakamura-Kuroda t10de 1
Page No.
128
128
128
128
134
137
143
6.2 BEHAVIOUR OF SLUDGE FLOW ALONG THE LOWER INCLINED SURFACE ... 147
6.2.1 t1echanisms of Sludge Flow 147
6.2.2 Some Relevant Parameters for the Layer t1ove-ment 152
6.2.2.1 Size of sludge solids 152
6.2.2.2 Density of the sludge solids 154
6.2.2.3 Liquid viscosity 156
6.2.2.4 Shape and surface texture of solids 158
6.3 OPERATING PERFORMANCE OF CONTINUOUS LAt~ELLA SEPA-TOR: THEORETICAL AND PRACTICAL ASPECTS 160
6.3.1 Introduction 160
6.3.2 t1aximum Handling Capacity for the Pure Clear Liquid Overflow... 161
6.3.3 Sludge Thickening Performance 183
127
CHAPTER 6
DISCUSSION OF RESULTS
6.1 EXPERIMENTAL VERIFICATION OF BATCH INCLINED SEDIMENTATION MODELS
6.1.1 Inclined Sedimentation Models of· Acrivos and Herbo1zheimer
The mathematical models developed by Acrivos and Herbo1zheimer
to describe the different types of settling behaviour in both low
and high aspect ratio separators have been verified experimentally.
Some realistic range of conditions under which the models are shown
to be valid have also been established. Details of the experimental
conditions and the various equations for predicting the profile of
the clear liquid/suspension interface and the velocity field in the
clear liquid layer are given in Appendices A.1.1 and A.1.2.
6.1.1.1 Low aspect ratio case
6.1.1.1.1 Steady-state clear liquid/suspension lnterface
It is observed that immediately after the commencement of settling,
a clear liquid layer is formed beneath the upper inclined surface
and whose thickness grows progressively with time until a steady
state condition is reached - from then onwards the thickness becomes.
stationary, i.e. independent of time. The only time dependent behaviour
is the fall of the top horizontal interface as shown by the i11ustra-
tion on the next page.
128
Steady-sta t~/.[~~~~~~~'" clear liqU~d/ suspension interface
---- transitional behaviour
-- steady-state behaviour
This overall settling behaviour is consistent with the theoretical
prediction. The time taken to reach steady state is relatively short,
by comparison with the overall settling time, and occurs only a few
seconds after the start of the settling process. It is to be stressed
that all the relevant measurements are made only after the attainment
of this steady state condition. Otherwise erroneous experimental
results would have been obtained and any subsequent comparison with
the theoretical steady state predictions would have produced wrongful
conclusions.
A comparison between the predicted and measured steady state
thickness of the clear liquid layer as a function of the distance
along the upper inclined surface is shown in Figures 6.1-6.3 (the
detailed experimental results are given in Tables A.l-A.15 and are
se If expl anatory). As can be seen. very good agreement indeed is
obtained throughout the range of experimental conditions tested.
III almost all cases the average level of agreement exceeds 80%, though
theory is shown to slightly underpredict the thickness. This is not
129
FIGURE 6.1: COMPARISON BETWEEN THE THEORETICAL AND MEASURED THICKNESSES OF THE CLEAR LIQUID LAYER ALONG IIiE UPPER INCLINED SURFACE OF A PARALLEL SIDED BATCH SEPARATOR Aspect ratio, h/b = 1.13
Angle of inclination, e = 600 (from the,vertical)
--- Theoretical line (Equation 4.16)
Distance along the u~per inclined surface, x(cm)
301iv /v 201sv /v 9 c
8 c •
7 . c x
6 c x
5
4
3
2
1 c
1 O%v /v
•
•
•
5~~v/v A
c.= 1% v/v
o
o
~ 1 particle diameter
o
O+-~--~--r-~--~ __ r-~--~-'---r--~~---r~ o 0.2 0.4 0.6 O. G 1.0 1.2 1. 4 1.6 1.8 2.0 2.2 2.4 2.6 2.8
Thickness of clear liquid layer, 0D(mm)
130
FIGURE 6.2: COMPARISON BETWEEN THE THEORETICAL AND MEASURED THICKNESSES OF THE CLEAR LIQUID LAVER ALONG IRE UPPER INCLINED SURFACE OF A PARALLEL SIDED BATCH SEPARATOR
Aspect Ratio, h/b = 3.42
e = 200
-- Theoretical line (Equation 4.16)
x(cm) 17 20%v/v
30%v/v 10%v Iv 5%vlv Co = 1% v/v
16 0 x A
0 x A
14 Cl ~ A 0
0 x • A 0
12 0 x • A 0
Cl x • A 0
10 Cl x • A 0
Cl x A 0
8 )\ A
x A
6
4
'--' 1 particle diameter
2
p
O+-~--~~--~~--,--,--,-~--~~r--r~ o 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 -2.0 2.2 2.4 2.6
Thickness of clear liquid layer, 0D(mm)
111
FIGURE 6~3: C011PARISON BETWEEN THE THEORETICAL AND I1EASURED THICKNESSES OF THE CLEAR LIQUID LAYER ALONG THE UPPER INCLINED SURFAcE OF A PARALLEL SIDED BATCH sEpARATOR
x(cm) 18
16
12
1
8
6
4
2
Aspect Ratio, h/b = 3.42
e = 300
--- Theoretical line (Equation 4.16)
30%v/v 20%v/vlO%V/v 5%v/v [] x • /l.
[] " • L:.
[] x • [] ~ • A
0 ~ .. ~ A
x A
x • [] x • A
o
o
c = l%v/v 0 0
0
0
0
0
0
0
0
0
0
0
0
0
I......J 1 parti cl e diameter
O~~--~--+-~--~--~~--~--~~--~~~~~ o 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8
Thickness of clear liquid layer, 0D(mm)
1 ~?
unexpected since the latter is based on an asymptotic analysis
(i.e. A ~ 00) and hence the predicted thickness should correspond
to a lower limit. Measurement errors are estimated to be small,
since the experimental data for the clear liquid layer thickness
can be accurately obtained from cine-films.
A summary of the experimental conditions under which the theo
retical model is shown to be valid is listed below:
aspect ratio, h/b = 1.13 and 3.42
1% v/v ~ Co ~ 30% v/v
7.61xl0 4 ~ Ao ~ 8.47xl0 7
0.17 ~ R • .;;; 2.12
One encouraging outcome, though unexpected, is that the theoretical
model gives equally good predictions even up to a concentration of
as high as 30% v/v. A possible explanation is that the application
of continuum mechanics, which forms the basis of the theoretical
model, remains valid even at such a high concentration. Furthermore,
it confirms the strong dependency of the settling process on large
values of A - the latter in fact becomes larger at a higher concen
tration. Though, in principle, there should exist a limiting concen
tration' above which the appl ication of continuum mechanics is expected
to breakdown, no attempt is made to determine that value.
As discussed in Section 4.2.1, the fact that steady state conditions
are attainable in a low aspect ratio separator reaffirms the feasibility
133
of using it on a continuous basis. More importantly, no addition
constraint need be imposed on the design to bring about the reali
sation of steady state because the latter is inherently attainable.
6.1. 11.2 Velocity field in the clear 1 iqOid layer
Detailed results for the measured velocities in the clear liquid
layer obtained using the Laser Doppler Anemometer are given in Tables . A.16-A.27. A comparison between the predicted and measured longitu-
dinal components of the liquid velocities shows an average agreement
of greater than 80%, and that provides further verification of the
theoretical model.
However, it is evident from the tables that in the majority
of cases the velocity measurements that are made along the thickness
of the clear liquid layer (i.e. 0D) are insufficient in number to
provide a complete verification of the predicted velocity profile.
This is because the clear liquid layer, being very small, imposes
a practical limit on the number of measurements that can be accurately
made. Two of the cases that provide a more complete comparison are
shown in Figures 6.4 and 6.5 for aspect ratios of 1.8 (a = 45°) and
3.78 (a = 20°) with Co = 1 and 2~% v/v. As can be seen, though the
theoretical model is capable of adequately predicting the overall
velocity profile, it tends to give a slight underprediction towards
the upper inclined surface; and an overprediction towards the clear
liquid/suspension interface. This discrepancy arises mainly because
the theoretical model underestimates the increasing viscous effect
towards the interface which tends to impede the liquid velocity around
134
FIGURE 6.4: COMPARISON BETWEEN THE PREDICTED AND MEASURED COMPONENTS OF LIQUID VELOCITY IN THE CLEAR LIQUID LAYER FOR A PARALLEL SIDED BATCH SEPARAIOR
10
8
~
V1 '-E E 6 ~
>, ...., .~
u 0 ~
(IJ 4 >
" .~
::> 0-.~
-'
2
o 0
8
~ .~
u 4 o ~
(IJ
>
.~
::> ~ 0- L .~
-'
o 0
Aspect ratio, h/b ~ 1.8 e ~ 45°
------ Predicted thickness of clear liquid layer •• ••.•. Experimentallydetermined velocity profile ------Predicted velocity profile (Equation 4.l2)
Co = 1 % v/v
I I
.' .·0,' ... 0. 1
..... 1
1
••••• {!j ••• I '. '1
I I I I I I
1 2
I I I I I I 2 o
. : . •
o
. . :
Co = 2~% v/v
I .. 0' .. '1
1
.0·····~ I I I I I I I I
I I I I I I I I I Position along the
upper inclined .2 surface, x = 8'. cm
Positiun along the upper inclined
2 surface, x = 6 cm
Position in the clear liquid layer, y(mm)
Position in the clear 1351iquid layer, y(mm)
FIGURE 6.5: COMPARISON BETWEEN THE.PREDICTEDAND MEASURED LONGITUDINAL COMPONENIS OF LIQUID VELOCITY-IN lAE CLEAR LIQUID LAVER FOR A PARALLEL SIDED BATCH SEPARATOR
Aspect ratio, h/b = 3_78 e = 20·
------- Predicted thickness of clear liquid layer "'-'-' Experimentally determined velocity profile --- Predicted velocity profile (Equation 4.12)
Co = 1% v/v Co = 2~% v/v 10
8 I tu-·'· - -0 .. 1 . . . I
I ~) .~
u "::4 I ClJ >
~
VI ...... " E ~
~ .~
u 0 ~
QJ
>
" . ~ " CT .~
...J
I I I
o ~O------~~----~~ 1 2
8 I .-0'" -.~
I 6 •
I . .
I --. 4 I
I 0
0 1 2
Position in the clear liquid layer, l(mm)
136
. . : --:
: -. -
0
o
I .. ' ... 0·.1
1
I '-"--~I
I I I I I
I I I I I I
Position in the clear liquid layer, y(mm)
2
' ..
Position along the upper inclined surface, x = 12 cm
Position along the upper inclined
2 surface, x = 8 cm
that region.
Nevertheless, the verified flow field in the clear liquid layer
will provide a reliable basis for developing a stability analysis
to define the factors responsible for initiating flow instability
at the clear liquid/suspension interface. It is already discussed
in Section 4.2.3 that the effects of flow instability, which is mainly
responsible for the re-entrainment of particles into the supernatant,
is one of the major problems associated with the use of a lamella
separator.
6.1.1.2 High aspect ratio case
In line with the theoretical prediction, it is found that under
certain experimental conditions it is not possible to attain a steady
state clear liquid/suspension interface along the entire length of
the separator. There exists a critical point of discontinuity above
which the interface is in perpetual transience: a steady-state con
dition is achieved only along the lower part of the separator below
that position of discontinuity.
Moreover, it is evident from the results in Table 6.1 that the
latter can in fact be adequately predicted by the existing theory
using Equation 4.18 - the dimensional form of which is given in Appen
dix A.l.2.2. To cite an example, in the case where the aspect ratio
is 64 and with c = 1% v/v, the predicted position of discontinuity . 0
is at x = 19 cm, which compares very favourably with the experimen-
tally determined at x = 15-20 cm. The latter is quoted in terms
of a range of x's rather than a discrete value because it is, in
137
TABLE 6.1: EXPERIMENTAL VERIFICATION OF THE POSITION OF DISCONTINUITY, Xc
High Aspect Ratio Case
Angle of Aspect Length Conc.of Predicted Experimentally i nc 1 i r Ratio of suspen- position of determined nation separator, sion disconti- position of
e (h/b) Xs (cm) (% v/v) nuity, discontinuity, xc(cm) (cm)
45° 64 105 1 19 ~' ... 15-20
2.5 60 45-50
5 148 * 10 334 *
"
15 640 *
, 30° 75 100 1 34 28-30
2.5 105 *
20° 41.31 51 1 53 * 5 407 *
" , , ,
* Discontinuity not found because the predicted position at which
it would have occurred lies beyond the actual length of the sepa-
rator, xs.
138
practice, difficult to detect the exact position where the discon
tinuous behaviour first occurs. It is strongly believed that this
uncertainty is largely responsible for the relatively poorer agree-
ment at 2~% v/v {see Table 6.1}.
However, in all the experiments where the concentration is greater
than 2~% v/v, no discontinuous behaviour is observed because the pre
dicted position at which it would have occurred lies beyond the actual •..
length of the separator that is used. Interestingly these results
imply that in the design of a continuous system the constrain~ on
the separator length, brought about by the requirements of steady state,
is less demanding on the high concentration applications than the
lower ones.
Furthermore, the thickness of the steady-state clear 1 iquid layer
that is formed below the discontinuity is also shown to be adequately
predicted by the theoretical model {refer Tables A.28-A.36}. A graphi-
cal comparison between the two at different positions along the upper
inclined surface are shown in Figures 6.6-6.8 for the aspect ratios
of 41.31 , 64 and 75 respectively. As can be seen, the agreement
between the predicted and measured values are very good indeed. The
only exception, though perhaps not very obvious from Figure 6.7, is
in the case where cd = 15% v/v. However, its detailed results in
Table A.34 will show that the average level of agreement betweeen
the predicted and measured values - though is about 75% - is still
significantly lower than those obtained under the rest of the experi
mental conditions that have been tested. The most probable explanation
is that the concentration limit for the theoretical model has been
nQ
FIGURE 6.6: COMPARISON BEHJEEN THE THEORETICAL AND r1EASURED THICKNESSES OF THE CLEAR LIQUID LAYER ALONG THE UPPER INCLINED SURFACE OF A PARALLEL SIDED BATCH SEPARATOR
x(cm) 50
45
40
35
30
25
Aspect ratio, h/b = 41.31 e = 70 0
-- Theoretical 1 ine (Equation 4.17) 5% v/v
A
o
t:. o
o
o
o
c = 1 % v/v o
20 t:.
15
L-J 2-particle diameter
10 o
o
5
o~----~----~----~------~----~~
o 1 2 3 4 5 5.5
Thickness of clear liquid layer, QD(mm)
140
FIGURE 6.7: COMPARISON BETWEEN THE THEORETICAL AND MEASURED THICKNESSES OF THE CLEAR LIQUID LAYER ALONG THE UPPER INCLINED SURFACE OF A PARALLEL SIDED BATCH SEPARATOR
x(cm) 85
80
70
60
Aspect Ratio, h/b = 64 e ,; 45 0
-- Theoretical line (Equation 4.l7)
l5%v/v lO%v/v. Co = ~ v/v
•
•
•
• "
•
" . 50 A
~ 2-particle diameter
40
J o 1 2 3 4 5
Thickness of clear liquid layer, 0D(mm)
141
FIGURE 6.8: COMPARISON BETWEEN THE THEORETICAL AND 11EASURED THICKNESSES OF THE CLEAR LIQUID LAYER ALONG THE UPPER INCLINED SURFACE OF A PARALLEL SIDED BATCH SEPARATOR
x(cm) 80
70
60
'50
40
0 T 0 1 2
Aspect Ratio h/b = 75 8 = 30°
--- Theoretical 1 ine (Equation 4.7)
c = 2~% v/v o A
A
~ 2-particle diameter
3, 4 5
Thickness of clear liquid layer, 0D(mm)
142
reached, since the latter is essentially developed for a dilute
settling system.
From a design pOint of view, the above experimental verifica
tion of the Acrivos and Herbolzheimer's flow model for the high aspect
ratio case further justifies its use as a guideline for establishing
the essential conditions of steady state when "designing a continuous
lamella separator. (A detailed account of this application is already
discussed in Section 4.2.1).
6.1.2 Experimental Verification of the Nakamura-Kuroda (N-K) Model
The N-K equation for predicting the rate of sedimentation in
an incl ined batch separator has beeri verified experimentally using
the suspension of glass beads described in Chapter 4 and Appendix
A.l.l. By contrast with the analyses of previous workers, which were
based on the rate of fall of the top horizontal interface, the sett
ling rate is in this case expressed in terms of the actual rate of
generation of clear liquid per unit width of the separator. The latter
is believed to provide a more direct and accurate measure of the actual
settling rate. Accordingly, the modified N-K equation that is used
in the calculations and the experimental method to determine the rate
of generation of clear liquid are given in Appendix A.l.3.
Table 6.2 provides a comparison between the theoretical and expe
rimental results for the initial settling rate of the above suspension
in a low aspect ratio batch separator. Clearly, under the range of
settling conditions tested:
143
TABLE 6.2: EXPERIMENTAL VERIFICATION OF THE PREDICTED RATE OF BATCH INCLINED SEDIMENTATION USING THE NAKAMURAKURODA EQUATION
Low Aspect Ratio Case
Aspect Angle of Conc.of Ao Ro Initial* rate of generation of clear Agreement bet-Ratio incl ination susp. liquid per unit width of separator ween experimen-
(from the (% v/v) (x 10 cm2/s) ta 1 and theore-verti ca 1 ) Experimental Theoreti ca 1 tical values
1.13 600 1 7.6lxl0" 0.70 5.10 4.95 0.97 5 5.82xl05 0.46 . 3.39 3.28 0.97
10 1.3lxl06 0.41 3.18 2.90 0.91 20 3.92xl06 0.27 2.18 2.10 0.96 30 9.24xl06 0.17 1.49 1.24 0.83
3.42 200 1 6.97xl05 2.12 3.25 2.91 0.90 5 5.32xl06 1.39 2.33 1.91 0.82
10 1.20xl07 1.23 2.04 1.69 0.82 20 3.59xl07 0.82 1.35 1.13 0.84 30 8.47xl07 0.52 0.89 0.72 0.81
3.42 300 1 6.97xl05 2.12 4.56 3.94 0.86 5 5.32xl06 1.39 3.11 2.58 0.83
10 1.20xl07 1.23 2.53 2.29 0.91 20 3.59xl07 0.82 1.85 1.54 0.83 30 8.47x)07 0.52 1.17 0.98 0.84
* These initial rates are not actually obtained at time zero but at 5 seconds after the commencement of settling. This brief period allows for the complete dissipation of any residual disturbances induced by ·the agitator when creating the homogeneous suspension prior to every test run.
i.e. 7.61xl04~<8.47xlO, 0.17<R<2.12, 200<6<600 and 1.13< ~ 3.42.
the agreement between theory and experiments is very good indeed. In
all cases the level of agreement exceeds 80%. These results are
consi stent with those obtained recently by Acri vos and Herbol zheimer2 ,
who also worked with non-flocculated, fully dispersed suspension.
The latter in fact obtained near perfect agreement between theory
and experiments. It should be noted that the experimental results •
reported in the table are liable to errors arising mainly during
the graphical analysis of the results. However, such errors are
estimated to be small and should only be about 1% of the reported
values. Taking this margin of errors into account it appears that,
though the N-K equation gives sufficiently accurate predictions, it
actually slightly underestimates the settling rate.
From a design standpoint the findings above have two significant
implications and these are summarised below:
i) in addition to having verified the predictive capability of the
N-K equation, they also provide some realistic conditions under
which the equation is shown to be applicable - in particular:
A = 0(104)- 0(107), and
R. = 0(1)
Since in most industrial applications A is typically 0(105) and
larger while R is small (i.e. 0(1 )-0(10)), it follows that the
145
N-K equation should, in principle, be adequate for the design
of both batch and continuous separators. It must, however, be
stressed that this assessment is based on the results of experi
ments using non-flocculated suspension. Before any generalisa
tion can be made the predictive capability of the N-K equation
will also have to be tested on flocculated suspensions.
ii) that the N-K equation is capable of providing accurate predictions
for the settling rate even up to a concentration of as high as
30% v/v. It should therefore serveas a useful design tool for
sizing lamella separators for both clarifying and thickening
applications. It is evident from industrial sources that though
the design of lamella separators for clarification duties can
be achieved adequately using existing techniques, difficulties
are commonly encountered when sizing such equipment for the
thickening applications.
Hence, there is now sufficient justification and incentive to
extend the use of the N-k equation to predict the throughput of a
continuous lamella separator. This will be the subject of discussion
in the subsequent section.
146
6.2 BEHAVIOUR OF SLUDGE FLOW ALONG THE LOWER INCLINED SURFACE
6.2.1 Mechanisms of Sludge Flow
It is found, from the batch scale experiments (details already
given in Section 5.3.3), that the flow of sludge along the lower
inclined surface is not continuous: instead it occurs via a sequence
of intermittent movements at various angles as the latter is progres
sively increased. Moreover, different types of sludge movements
are -involved depending on the thickness of the 1ayer* and the nature
of its constituent solids.
On the whole, three distinct types of sludge flow behaviour
have been identified and these are classified as layer movement,
heap movement and bulk movement. Their individual flow characteris
tics are summarised as follows:
i) Layer Movement
This mode of sludge transport (see Figure 6.9c) is brought
about by the overlying layers of sol ids sl iding over a relatively
thin and almost stationary bottom layer (i.e. approximately 1-2
particle diameter(s) in thickness). By analogy, the gross behaviour
resembles the flow of a viscous fluid down an inclined surface,
retarded at the wall by a thin boundary layer. Moreover, the move
ment of the top layers appears to exhibit a flat vertical velocity
profile (i.e. plug flow behaviour).
* see overleaf
147
.
In the present analysis the initial sludge layer thickness is
expressed in terms of the number of particle diameters via Co - the
initial concentration of the suspension that is used to create the
sludge layer. For the two sizes of solids used in the experiments
the estimated thicknesses of the initial sludge layer at various
concentrations (co) are tabulated below:
Initial Concentration of Estimated Sludge Layer Thickness Suspension, co' (% v/v) (Number of particle diameters)
Size I: 90-125 ~m Size 11: 355-420
0.1 1 (monolayer)
0.2 1-2
0.3 2-3 Monolayer
0.4 3-4
0.5 4-5
1.0 8-9 2~3
1.5 12-13 3-4
~m
It should be noted that in determining the thickness, a porosity of 0.5
for the sludge layer is assumed.
lN3~3hOW H3AVl :(J) lN3W3AO~l dV3H : (q)
. t-·t,.t 1; " ' ,t
l' 1·" f/ . .. 't :' 1 l,
t , 1 l
~. ~~t . r t·,t i.oS t~ j-t.: I,
' • ...t ,t ~. !..J Nr 't~. tf.~ t ,\" K .. ,~t ....
"~I ' ,"t H.tt \ • i~~t "f" ., ~.. ~.., \ ~.
,..(1 t·· i .t , .. ...t nt .-t.i ~
t \ 1
1'\3IA NV1·d
M01~ 3S001S 30 SWSINVHJ3W lN3a3~~IO 3Hl :6'9 3aOSI~
lN3W3l1OW )llna: (I!)
t f t t t t
t t ' .. t ... J
...... t, ,~
' ... ,t . .. ,t ...
...... .J_
'" ... ~
.. /.: 0;1 , . "
~.~--~--------.. --.......... ~, ....... \
ii) Heap Movement
In marked contrast with the layer movement, the sludge flow
in this case occurs in small aggregates (heaps) of solids over the
whole inclined surface. Its appearance, from a plan view, is clearly
illustrated in Figure 6.9(b).
iii) Bulk Movement
The prominent feature of the bul k movement, (as shown in Fi gure
6.9a), which distinguishes it from the first two cases is that the
entire sludge layer moves en masse. As such it resembles the
sliding motion of a solid block down an inclined plane.
Ha ving described the different sl udge movements, reference
is'now made to Table 6.3 that outlines the various types of overall
flow behaviour exhibited by the fully dispersed systems that have
been tested. As mentioned earlier, the sequence of sludge movements
that occur are clearly dependent on the concentration, co' and the
nature of the solids comprising the sludge. For example, the irre
gularly shaped solids (i.e. powdered glass, zircon and limestone) .
exhibit only heap and layer movements, whereas the spherical ones
(i.e. glass beads and bronze spheres) are also subjected to bulk
movement. Furthermore the layer movement is shown to occur only
at a higher concentration.
Hence, from a design point of ,view, there are those three possi
ble flow conditions to consider when sizing a lamella separator
as they will give different rates of sludge discharge. However,
for most practical applications the predominant mode of transport
150
TABLE 6.3: SLUDGE FLOW BEHAVIOUR OF THE DIFFERENT FULLY DISPERSED SYSTEMS
Dispersed System Size Range Sequence of Intermittent Sludge Layer Movements (with Progressive Incr'!ase in a) of Solids Initial Concentration of Suspension, Cn, from which the Sludge Layer is Formed
Liquid Solids (\lm) 0.1% v/v 0.2% v/v 0.3% v/v 0.4% v/v 0.5% v/v 1.0% v/v I 1.5% v/v
Water Glass 355-420 Bulk Heap Movement-+!3ulk Hovement Layer Hovement-+!3ulk Movement beads Movement
Water Gl ass. 90-125 Heap + Bulk Layer + Heap + Bulk beads Hovement Hovement Movement Movement Movement
Water Bronze 90-125 HealBulk Localised HeaprBulk Layer + Heap + Bulk spheres Move-Hove- Layer ->0 Move-~love- Movement Movement I~ovement
ment ment Movement ment ment
Water Powde- 90-125 Heap Move~nt Localised + Heap Layer + Heap red Layer Movement Hovement Hovement glass Movement
Water Zi rcon 90-125 Localised Heap Layer Movement + Heap Movement Layer ...... Hovement Hovement
Water L ime- 90-125 Loca 1 i sed Heap Layer Hovement + Heap Movement stone Layer -+- Movement
Movement Reofos 65/ Glass 90-125 Heap Movement + Bulk Movement Layer + Heap + Bulk Reomol DBP beads Movement Movement Movement
will approximate to layer movement, since the sludge layer is usually
of the order of a few particle diameters in thickness. It is there
fore believed that for the general purpose of design, a mathematical
model based purely on layer movement should be adequate. This is
substantiated by the fact that in all the experiments where layer
movement prevails, the latter alone accounts for the removal of
about 80-90% of the total sludge layer from the inclined surface.
The subsequent heap and (or) bulk movements •. as indicated in Table
6.3, play only a secondary role in removing the remaining quantity
of sludge. A further justification is provided by the fact that
when matching the batch flow behaviour with the continuous one,
the latter actually approximates to layer movement.
Some relevant parameters for the layer movement have also been
identified to provide the basis for a mathematical model. They
will be discussed in the next section.
6.2.2 Some Relevant ParameterS for the Layer Movement
6.2.2.1 Size of· Sludge· solids
The relevance of solids size as a parameter governing the layer
movement is shown by the experimental results in Table 6.4. Two
size ranges of the same spherical glass beads have been used for
this purpose: 90-125 ~m and 355-420 ~m.
152
TABLE 6.4: EFFECT OF SIZE OF SOLIDS ON THE LAYER MOVEMENT
Initial concentration Required angle of inclination for layer of the suspension movement, ,,0
that is used to form 355 -4'))jJm glass beads '10-\as jJm glass beads the sludge layer, in distilled water in distilled water
Co (% v/v)
0.5 200 17.50
1.0 190 17.00
1.5 18.50 . 17.00
As can be seen, at any given concentration co' the angle at which the
layer movement occurs is evidently lower for the smaller size range.
The reason being that in the latter case there are more overlying
layers of solids present at the same concentration to provide a
stronger impetus for layer movement to occur - see illustrations
below. The whole transport phenomenon resembles a layered chunk
of solids sliding over a thin and almost stationary bottom layer.
Sliding mass of overlyi ng soli as
Di recti on of sludge flow
Thin and relatively stationary bottom layer
Smaller glass beads (90-125 jJm): Thicker overlying layer of solids
153
Direction of sludge flow
Larger glass beads (355-420 ~m): Thinner overlying layer of solids
6.2.2.2 Density of the Sludge Solids
Since the flow of sludge along the inclined surface is dependent
on a sufficiently large gravitational force, the required angle of
inclination for layer movement to occur is expected to be lower for
the denser solids than the lighter ones. However, as shown in Table
6.5, the reverse situation actually occurs. Despite the fact that
the bronze spheres are denser than glass beads by greater than a fac
tor of 3, the required angles of inclination for layer movement are
consistently higher over the range of concentrations from 0.5 to
1.5% v/v.
154
TABLE 6.5: EFFECT OF SOLIDS DENSITY ON THE REQUIRED ANGLE OF INCLINATION FOR LAYER MOVEMENT
*
Initial concentration Required angle of inclination for of the suspension layer movement, aO
that is used to form the sludge layer, Bronze spheres*
Co (% v/V) in distilled water
0.5 220
1.0 190
1.5 18.50
Size range of solids = 90-125 ~m Density of bronze spheres = 7700 kg/m3
Density of glass beads = 2460 kg/m3
Glass beads* in distilled water
17.50
17.00
]7 .00
The most likely explanation is that, because of its higher solids
density, the initial sludge layer of the bronze spheres that is formed
tends to be more compact - possibly forming something close to a cake
structure - and hence the inclination angle required to cause the
initial layer movement is higher than that for the lighter glass beads.
In view of the conflicting results, further investigation is needed
to either reaffirm or refute the above hypothesis as it has signi
ficant implications on some existing design practices. For example,
Forsell and Hedstrom18 appear to specify the required angle of incli
nation- for a lamella separator based purely on the sludge densities
without considering the influence of interparticle reactions. In
the meantime, prudence is called for when applying the latter approach
because it may in some cases be oversimplistic in nature.
155
Initial sludge layer of bronze spheres (relatively more compact)
6.2.2.3 Liquid Viscosity
Initial sludge layer of gl ass beads (relatively loose)
It seems fairly obvious that 1 iquid viscosity ~Ii 11 have a
significant effect on the flowability of the sludge layer. This
is because a more viscous liquid exerts a stronger viscous resistance
to the movement of the sludge layer tending to reduce its flow rate.
The results in Table 6.6, which are obtained using the fully dis
persed systems of glass beads in the Reofos 65/Reomol DBP mixture
and distilled water, confirm the influence of the viscous effect
highlighted above.
156
TABLE 6.6: EFFECT OF LIQUID VISCOSITY ON LAYER MOVEMENT
Initial concentration Required angle of inclination for of the suspension layer movement, aO
that is used to form the sludge layer, Gl ass beads* in Glass beads* in
Co (% v/v) Reofos 65/Reomol DBP di still ed water
0.5 230 17.50
1.0 230 17.00
1.5 220 17.00
Note: * Size range of glass beads: 90-125 ~m Viscosity of Reofos 65/Reomol DBP mixture @ 250C = 22.2528 cp Viscosity of distilled water @ 250 C = 0.896 cp
The required angles of inclination for layer movement using the more
viscous plasticisers mixture are consistently 5-6 degrees higher than
that using d.istilled water. Moreover, the rate of sludge discharge
along the lower inclined surface is observed to be very much slower
in the former case. Unfortunately, no attempt has been made to
measure the actual sludge discharge rate because of time constraint.
Nevertheless the significance of liquid viscosity has been demonstra-
ted.
Furthermore, it is shown by the results in the table that layer
movement appears to be little affected by changes in concentration
(i.e. 0.5-1.5% v/v). This is because any effective increase in the
gravitational acceleration to the sludge layer is counterbalanced
by a corresponding increase in its effective viscosity.
157
6.2.2.4 Shape and Surface Texture of Solids
The effect of shape and surface texture of the sludge solids
on the required angle of inclination (~o) for layer movement is
shown in Figure 6.10. It is relevant to note that all the solids
used have been sized to the range of 90-125 ~m using standard
sieves.
The great difference in the required inclination angles for
the irregularly shaped solids (i.e. zircon, powdered glass and
limestone) and the spherical glass beads suggests that surface
texture and shape are important parameters. This is reinforced
by the fact that over the concentration range of 0.5-1.5% v/v,
the required ~ for the powdered glass is approximately 8~-9~ degrees
higher than that required by the glass beads, even though the former
has a slightly lower density, i.e. 2.21 g/cc versus 2.46 g/cc. How
ever, a similar comparison amongst the irregularly shaped solids
cannot be made because their exact shape factors have not been
defined.
158
FIGURE 6.10: EFFECT OF SHAPE AND SURFACE TEXTURE OF SLUDGE
SOLIDS ON THE LAYER MOVE~'ENT
o Zircon (90-125 ~m)
Li~estone (90-125 ~m)
Powdered glass (90-125 ~m)
• Glass beads (90-125 ~m)
Inclination angle required for layer movement, ~o (measured from the horizontal)
35
25
20
15
la
T o 0.5 1.0 1.5
Initial concentration of sysrension used to create the sludge layer:,: Co (% v/v)
159
6.3 OPERATING PERFORMANCE OF CONTINUOUS LAMELLA SEPARATOR: THEORETICAL AND PRACTICAL ASPECTS
6.3.1 Introduction
The inadequacies of the existing design methods 20 ,33,48,70 for
lamella separators have already been discussed in Chapters 1 and 4.
To reiterate, one of the major problems is the seeming inability to
predict, with sufficient accuracy, the actual operating capacity of
the continuous separator. It is commonly reported in the literature
that theory tends to overpredict the separator capacity by a factor
of 2, and sometimes even greater. Though it has been claimed by
'previous workers33,48 that the discrepancy is attributed larg~ly to
stability problems and mixing within the settling channels, it is
believed that there may be other significant causes of discrepancy
that have been neglected~ The latter include:
I) the inadequate provision of operating requirements for achieving
the essential steady-state conditions within the settling
channels - the negative repercussions have been discussed in
Section 4.2.1, and
11) the application of the theoretical models,beyond their limits
of validity. In most cases this problem arises because the
models contain too many simplifying assumptions, with the end
result that their applications become rather restrictive.
Furthermore, and for the same reason, their limits of validity
are often not theoretically definable.
160
In order to verify the above supposition and also as a step
towards developing an improved procedure for the lamella separator
design, all the present experiments are conducted under controlled
conditions* to suppress the potential causes of discrepancy due to
(I) and (11). In fact, it will be shown in the next section that
under these controlled operating conditions the general level of
agreement between theory and experiments is indeed significantly
much higher than that obtained by previous workers. Where devia
tions from theory exist in the present analysis, the causes of
discrepancy can now be safely attributed mainly to flow instability
and mixing problems. Photographic evidence is available to sub- .
stantiate this claim.
6.3.2 Maximum Handling Capacity for the Pure Clear..Liquid Overlow
In this series of experiments, the optimum performance of the
continuous separator - assessed in terms of its actual achievable
* As part of the controlled conditions, the dimensions of the continuous separator are chosen to satisfy the steady-state criterion given by Equation 4.18.
Furthermore, the operating conditions of the experiments are within the range of validity of the Nakamura-Kuroda equation that will be used to predict the maximum overflow rate. The latter has been established during the earlier batch experiments (refer Section 6.1.2).
maximum overflow rate* - is examined under different operating
conditions. The investigation is intended to serve a dual purpose,
the first of which is to establish the practical design limitations
for ensuring high separating efficiencies.
Secondly, to provide a comparison between the actual maximum
overflow rates with those predicted using the Nakamura and Kuroda
equation, in order to evaluate its potential use as a sizing tool . for design purposes. All the detailed results that have been obtained
are tabulated in Tables A.37-A.44, under Appendix A.2.
A comparison between the predicted and the actual maximum over
flow rates for the different modes of operation is shown in Table 6.7
for the case where the feed concentration (co) is 0.5% v/v and the
channel spacing of the lamella separator is 3.4 cm. For the purpose
of clarity and convenience of discussion, the major points are listed
below: .
*
i) In all cases, excellent agreement is obtained with the shorter
channel lengths (i.e. L = 49 cm and 66 cm) over the entire
range of inclination angles (eo) from 20 to 60 degrees.
As a basis for comparing the results of different experiments, this maximum rate is fixed as that flow rate at which the solids carry-over in the overflow is no greater than approximately 40 ppm. This corresponds to a registered reading of about 7NTU on the Hach Turbidimeter, as compared to its background value of 6NTU.
162
TABLE 6.7: ACCURACY OF THE NAKAMURA-KURODA EQUATION IN PREDICTING THE MAXIMUM OVERFLOW RATE (Qo) AT Co = 0.5% v/v FOR THE DIFFERENT MODES OF OPERATION
Inclination Angle
Channel spacing, b = 3.4 cm Channel width, W = 4 cm
Channel Aspect Ratio Length of ' .
.. (Q~)e~perim~ntal . (Qoltheoretical·
e(oh (cm) Separator . Locurrent~ LOcurrent~ Lounter-...... -Super-crit ita 1 . Subcritical current
60° 49 7.21 l.00 1.00 1.00 66 9.71 l.00 0.98 0.95 95 13.97 0.96 0.95 0.80
112 16.47 0.90 0.90 0.81
45° 49 10.19 1.01 0.99 0.99 66 13.73 1.00 0.96 0.95 95 19.76 0.95 0.93 0.90
112 23.29 0.89 0.88 0.85
30° 49 12.48 1.07 1.02 1.05 66 16.81 1.06 1.02 1.01 95 24.20 0.93 0.86 0.82
112 28.53 0.92 0.88 0.85
20° 49 13.54 l.03 1.03 0.96 66 18.24 1.05 1.00 0.94 95 26.26 0.80 0.76 0.76
112 30.95 0.90 0.81 0.80 . - - -
t eO: Measured from the vertical
163
ii) However, substantial deviations from the predicted overflow
rates arise when using the longer channel lengths of 95 cm
and 112 cm. Under these circumstances, the Nakamura-Kuroda equa
tion is shown to overpredict the maximum overflow rates. Never
theless, it should be stressed that the level of agreement is
still generally much greater than 80%, and hence the N-K equa
tion is still adequately applicable.
iii) The coccurent-supercritical mode is shown to produce consistently
higher maximum overflow rates than both the countercurrent flow
and the cocurrent-subcritica1 mode.
Photographic evidence (Figures 6.11 and 6.12) shows that with
the longer channel lengths, lower than expected maximum overflow
rates are obtained because of the re-entrainment of particles from
the suspension layer into the clear liquid stream. This finding is
consistent with that discovered by previous researchers, notably
Probstein and his co-workers. However, it is believed that the present
attempt is the first to study such an effect under more controlled
conditions. The latter negates other possibilities, such as the
occurrence of unsteady-state conditions within the settling channels,
which can also give rise to the re-entrainment of particles.
Furthermore, different mechanisms are found to be responsible for
the re-entrainment of particles under the various modes of operation.
In the case of the countercurrent flow and the cocurrent-subcritica1
mode, the two principal causes are:
164
i) an unfavourable velocity field at the vicinity of the clear
liquid/suspension interface which drags part of the suspension
layer along the direction of the clear liquid stream (Figure
6.11a). Reference is made to Section 4.2.3 for a detailed
account on this effect, and
ii) disruptive interfacial wave activity, which results in the
mixing of the already separated suspension layer with the
clear liquid layer (Figure 6.11b). However, it is observed
that the above effect is localised around the interfacial
region: the inner suspension layer appears to be relatively
unaffected.
On the other hand, the carry-over of particles in the super
critical mode arises because of flow instability that affects the
entire thickness of the suspension layer, and not just localised
at the interface as in the previous case. The latter is found to be
initiated by the formation of interfacial waves that grow progres
sively along the direction of the cocurrent flow until breaking
point, whence particles are literally ejected into the clear liquid
stream (see Figure 6.12b). Particle re-entrainment therefore ori
ginates mainly at the lower end of the separator, though it also
occurs at the fringes of the earlier unbroken waves, higher up the
separator, where they are exposed to the main flow stream in the
clear liquid layer. Figure 6.12a shows the earlier period of the
wave formation before wave breakage occurs, hence the more rounded
profile.
165
FIGURE 6.11{a):
---
RE-ENTRAINMENT OF PARTICLES INTO THE CLEAR LIQUID LAYER DUE TO UNFAVOURABLE VELOCITY PROFILE (coUNTERCURRENT fLOW)
----. ----. ----. - ---.,., - --~ ----'-_. ---.....
FIGURE 6.11{b):
---P' ---+ --+
RE-ENTRAINMENT OF PARTICLES DUE TO THE COMBINED EfFECTS OF AN UNFAVOURABLE VELOCITY PROFILE AND INTERFACIAL INSTABILITY (COUNTERCURRENT FLOW)
---+ -----~ --,. -----. ---. ---.." ---
166
. - - ---"" ,~ , """ I '
I
· '.~ ,. .: , ,:~ '(
, I
FIGURE 6.12{a): FORMATION OF '~INTERFACIAL WAVE" DUE TO FLOW INSTABILITY
JCOCURRENT-SUPERCRITlCAL MODE)
FIGURE 6.12{b): RE-ENTRAINMENT OF PARTICLES INTO THE CLEAR LIQUID LAYER DUE TO WAVE BREAKAGE BROUGHT ABOUT BY FLOW INSTABILITY (COCURRENT-SUPERCRITICAL MODE)
..... _-
•
FIGURE 6.12(a): FORMATION OF ~INTERFACIAL WAVE" DUE TO FLOW INSTABILITY
jCOCURRENT-SUPERCRITICAL MODE)
FIGURE 6.12(b): RE-ENTRAINMENT OF PARTICLES INTO THE CLEAR LIQUID LAYER DUE TO WAVE BREAKAGE BROUGHT ABOUT BY FLOW INSTABILITY (COCURRENT-SUPERCRITICAL MODE)
167
•
It is believed that the supercritical mode of operation gives
consistently higher maximum overflow rates than both the subcritica1
mode and the countercurrent flow because of its relatively more
stable nature. Moreover, unlike the latter two cases, the super
critical mode has an inherently more favourable velocity field that
actually drags part of the clear liquid layer at the interface
along the direction of the main flow, thus helping to stabilise
the settling particles around that region. A more detailed account
on this reversed flow field is given in Section 4.2.3.
Table 6.8 is meant to compare the effect of feed concentration
on the actual achievable overflow rates when the former is increased
from 0.5% v/v (Table 6.7) to 2% v/v. As can be seen, equally
e.xcellent agreement is obtained between the predicted and the
actual maximum overflow rates for the shorter channel lengths of
49 cm and 66 cm. However, with the longer channel lengths (i.e. L=95 cm
and 112 cm) substantial deviations from theory are obtained and which
worsen with increase in the feed concentration. The levels of agree
ment in both cases, over the entire range of operating conditions
tested, are summarised below:
Feed concentration (% v/v)
0.5
2.0
Actual maximum overflow rate as percentage of predlcted (%)
76-96
64-81
These results emphasise the preference for shorter channel lengths
when designing a continuous lamella separator for the higher concentra
tion duties because of the potentially more pronounced effects of
TABLE 6.8: ACCURACY OF THE NAKAMURA-KURODA EQUATION IN- PREDICTING THE MAXIMUM OVERFLOW RATE (Qo) AT c~ = 2% v/v FOR THE-DIFFERENT MODES OF OPERATION
Inel ination Angle e (0)
600
450
300
200
Channel spacing, b = 3.4 em Channel width, W = 4 cm
(Qo)experimental Channel Aspect (Qo)theoretical Length Ratio
(em) of Separator .L.oeurrent- L.oeurrent-
Supercritica1 Subcritical
49 7.21 1.01 0.99 66 9.71 0.99 0.99 95 13.97 0.78 0.73
112 16.47 0.69 0.66
49 10.19 1.02 1.00 66 13.73 1.02 0.99 95 19.76 0.81 0.70
112 23.29 0.71 0.64
49 12.48 1.00 0.98 66 16.81 0.99 0.97 95 24.20 0.75 0.69
112 28.53 0.71 0.66
49 13.54 0.99 0.98 66 18.24 1.00 0.98 95 26.26 0.78 0.78
112 30.95 0.76 0.72
169
counter-current
0.99 0.99 0.72 0.65
0.99 0.99 0.72 0.65
0.98 0.97 0.70 0.65
0.97 0.95 0.76 0.70
flow instability and mixing. A similar conclusion has recently
been obtained by Leung34 , based on a semi-empirical linear stability
analysis.
The effect of channel spacing, b, on the separator performance
is shown by the comparison of results in Tables 6.9 and 6.10 between
b = 1.S cm and 3.4 cm for Co = O.S% v/v and 2% v/v. It is found that
decreasing the channel spacing gives rise to stronger flow instability . and hence a corresponding reduction in the overall separation effi
ciency. This accounts for the very much poorer agreement between
the predicted and the actual maximum overflow rates. In particular,
at Co = 2% v/v and b = 1.S cm, the level of agreement drops to
only SO-70 percent. Clearly these results imply that for any
given application there exists a lower limit on the channel spacing
for achieving optimum performance.
It should, however, be pointed out that the above comparison
is only done for the countercurrent flow because of the limitations
of the continuous separator which restrict its operation in the
subcritical and supercritical modes at b = 1.S cm.
Optimum Aspect Ratio
So far the discussion ;s centred on two important design consi
derati ons:
i) the predi ct,,,,, capabi 1i ty of the Nakamura and Kuroda equati on,
and
TABLE 6.9: ACCURACY OF THE NAKAMURA~KURODA·EOUATION IN PREDICTING THE MAXIMUM OVERFLOW· RATE (00) FOR COUNTERCURRENT FLOW WITH CHANNEL SPACINGS OF 1.5 cm AND 3.4 cm AT Co = ~% v/v
Channel width, W = 4 cm
Aspect (Oo)experimental Inclination Channel (Oo)theoretical
Ang6e Length Ratio of a ( ) (cm) • Separator b = 3.4. cm. .b ".1.5 cm ,
600 49 7.21 1.00 0.85 66 9.71 0.95 0.81 95 13.97 0.80 0.77
112 16.47 0.81 0.69
450 49 10.19 0.99 0.79 66 13.73 0.95 0.74 95 19.76 0.90 0.72
112 23.29 0.85 0.65
300 49 12.48 1.05 0.82 66 16.81 1.01 0.71 95 24.20 0.82 0.66
112 28.53 0.85 0.65
.
200 49 13.54 0.96 0.89 66 18.24 0.94 0.78 95 26.26 0.76 0.67
112 30.95 0.80 0.65
171
TABLE 6.10: ACCURACY OF THE NAKAMURA-KURODA EQUATION IN PREDICTING THE MAXIMUM OVERFLOW RATE (Qo) FOR COUNTERUCRRENT FLOW WITH CHANNEL SPACINGS OF 1.5 cm AND 3.4 cm AT Co = 2% v/v
Channel width, W = 4 cm
Inclination Channel Aspect (Qo)experimenta1 Angle Length Ratio of (QoJtheoretica1 e (0) (cm) Separator
b = 3.4 cm b= 1.5 cm
600 49 7.21 0.99 0.64 66 9.71 0.99 0.60 95 13.97 0.72 0.58
112 16.47 0.65 0.57
450 49 10.19 0.99 0.63 66 13.73 0.99 0.65 95 19.76 0.72 0.56
112 23.29 0.65 0.56
300 49 12.48 0.98 0.65 66 16.81 0.97 0.65 95 24.20 0.70 0.58
112 28.53 0.65 0.50
200 49 13.54 0.97 0.70 66 18.24 0.95 0.62. 95 26.26 0.76 0.60
112 30.95 0.70 0.56 ..
,.
172
ii) the causes of deviation, from theory, of the actual achievable
maximum overflow rates under different operating conditions.
The ensuing discussion deals with the implications of those findings
on the separator design: in particular, the need to impose an
upper limit on the channel length in order to achieve high sepa
rating efficiencies.
Though it is generally realised that the use of an excessively
long separator is counterproductive because of the potentially
severe problem of particle re-entrainment, no previous attempts
have been reported to establish the optimum length. Yet it is
clear that with the latter, improved separator performance should
be achieveable.
Using the present experimental data, the order of magnitude of
the optimum length has been established via a plot of the actual
maximum overflow rate versus the aspect ratio* of the separator
(Figures 6.13-6.18). In general, there are essentially 3 regions
depicting different levels of separating efficiencies, as indicated
by the illustration on the next page.
* The aspect ratio is chosen instead of the channel length because of its increasing use to describe the geometry of a lamella separator.
173
Maximum overflow rate (Q ) o
® CD .: ..
Aspect ratio (h/b)
It should, however, be pointed out that on some of the plots, these
different regions may not be clearly defined becaus!! of insufficient
data - especially with Co = 0.5% v/vat e = 600 and 450.
Region I
Here, excellent agreement is obtained between the predicted
and the actual maximum overflow rates (Tables 6.7-6.10). Stable
flow conditions prevail and the problem of particle re-entrainment
is averted because any interfacial wave disturbance that is generated
does not amplify to breaking point, since the channel length is
relatively short. For the purpose of later discussion this region
of optimum performance will be defined by the aspect ratio (h/b)op.
Under the present experimental conditions and with b = 3.4 cm, this
corresponds to an optimum length of about 66 cm. However, with the
narrower spacing of 1.5 cm, the optimum length becomes less than
49 cm because of the potentially more pronounced effects of flow
i nstabil ity.
Regi on II
This region marks the beginning of significant particle re
entrainment, and hence the maximum separating efficiency is not
achievable. For the reasons already explained earlier, the problem
gets progressively worse with increase in the channel length. This
explains why on the Qo versus h/b plot, the slope of the curve
becomes gentler at the higher aspect ratio.
Regi on I II
Because the conditions for the occurrence of extreme particle
re-entrainment are already present at this stage, further increase
in the channel length appears to produce no significant increment
to the achievable maximum overflow rate. In fact, in some cases
a slight decrease is obtained. This region therefore marks the
uppermost limit for the channel length that should be used for
design purposes. Exceeding this limit will be uneconomic because
of the diminishing return in Qo' Again, for the purpose of later
discussion, this uppermost limit on the separator length will be
referred to in terms of the aspect ratio as (h/b)Ul'
Summarised below are the estimated values of (h/b)UL obtained
from Figures 6.13-6.18 for the two feed concentrations of 0.5% and
2% by volume. (The channel spacing of the lamella separator is in
this case 3.4 cm).
175
FIGURE 6.13: EFFECT OF SEPARATOR ASPECT RATIO ON THE ACTUAL MAXn·;UM
OVERFLOW RATE FOR THE COUNTERCURRENT FLOW WITH
Co = 0.5% v/v, b = 3.4 cm AND e = 200 -600
Inclination angle (eo) 60°
o 45°
x 30°
o 20°
Maximum overflow rate, Qo (cc/min) 700
600
5 10 15 20 25 Aspect ratio of separator (h/b)
176
o
30 35
FIGURE 6.14: EFFECT OF SEPARATOR ASPECT RATIO ON THE ACTUAL MAXIMUM OVERFLOW RATE FOR THE COCURRENT-SUBCRITICAL MODE WITH Co = 0.5% v/v, b = 3.4 cm AND e = 200-600
Inclination angle (e)
60°
45°
x 30°
o 20°
Maximum overflow rate, Qo (cc/min)
700
o 5 10 15 20
Aspect Ratio of Separator (h/b)
177
o
30 35
FIGURE 6.15: EFFECT OF SEPARATOR ASPECT RATIO ON THE ACTUAL MAXIMUM OVERFLOW RATE'FOR THE COCURRENT-SUPERCRITICAL MODE WITH c = 0.5% v/v, b'='3.4'cm AND e = 200-600 ,0
o
)(
o
inclination'angle (e) 60 0
45°
30°
20°
Maximum overflow rate, 00
(cc/min)
700
600
500
400
300
200
100 '
5 10 15 20 25
Aspect Ratio of Separator (h/b)
178
o
o
o
FIGURE 6.16: EFFECT OF SEPARATOR ASPECT RATIO ON THE ACTUAL MAXIMUM':
o
o
OVERFLOW RATE FOR THE COUNTERCURRENT FLOW WITH Co = 2% v/v, b = 3.4 cm AND 8 = 200-600
Inclination·angle (8)
Maximum overflow rate, Qo (cc/min) 700
600
500
400
300 c
200
100
O~ ____ ~ ____ ~ ____ -L ____ ~ ____ -J ______ L-__ ~
o 5 10 15 20 25 30 35 Aspect Ratio of Separator (h/b)
179
FIG:URE 6.17: EFFECT OF SEPARATOR ASPECT RATIO ON THE ACTUAL MAXrr·1UM
OVERFLOW RATE FORTHECOCURRENT-SUBCRITICAL MODE WITH Co = 2% v/v, b = 3.4 cm AND 6 =200-600
Inclination angle (6)
o
x
o
Maximum overflow rate, Qo (cc/min) 700
600
500
5
o
10 15 20 25 Aspect Ratio of Separator (h/b)
180
30 35
FIGURE 6.18: EFFECT OF SEPARATOR ASPECT RATIO ON THE ACTUAL MAXIMUM OVERFLOlf RATE FOR THE COCURRENT -SUPERCRITICAL MODE WITH Co = 2% v/v, b = 3.4 cm AND 8 = 200-600
Inclination angle (8)
c
x
o
Naximum overflow rate, Qo (cc/mirii
700
600
500
400
300
200
100
o
o
o ~----~----~----~------~----~----~----~ o 5 10 15 20 25 30 35
Aspect Ratio of Separator (h/b)
181
Co (% v/v)
0.5
2.0
(h/b)UL
25-30
15-22.5
Evidently, for Co = 2% v/v, the uppermost limit for the separator
aspect ratio is considerably lower, hence reinforcing the earlier
finding that a shorter channel length should be used for the higher
concentration duties. Perhaps of greater importance is the revela-
tion that the above limits are far below the actual aspect ratio
advocated by the existing design for a lamella separator of similar
channel spacing, i.e. where (h/b)design is specified as ranging from
40-50. This is despite the fact that the present experimental
results are obtained using ideal suspensions.
Thus the implication is that the eXisting design recommendation
for the-separator aspect ratio is unacceptably high. Consequently the
latter should be scaled down before any hope for improvement to the
overall separating performance can be realised.
182
6.3.3 Sludge Thickening Performance
The predominant mechanism of sludge transport along an
inclined surface has been established in Section 6.2 as that due
to layer movement. Though it is conceivable that increasing the
inclination angle, ~, to provide a greater gravitational accel
eration should enhance the layer movement, an overprovision is
in fact counter productive. This is because of the consequent
decrease in the solids handling capacity of the separator resul-
ting in smaller sludge layers, which in turn impedes the transport
of sludge due to layer movement. Hence, there should, in principle,
exist an optimum angle of inclination at which both the gravitatio
nal effect and the mechanism responsible for layer movement are
optimised.
The determination of such an optimum inclination angle,
(~)oPtimum' is the object of this part of the thesis. Its verifica
tion should serve two purposes:
i) to provide the basis for a general optimisation step to
upgrade the existing lamella separator design, and
ii) to further sUbstantiate layer movement as the predominant
mechanism of sludge discharge, in order to justify its use
as a basis for a mathematical model.
Thus, in a series of experiments the effect of inclination
angle on the sludge thickening performance is determined. The
latter is judged by the consistency and the actual achievable
183
solids concentration, cu' in the underf10w stream. The influence
of different flow patterns are also investigated based on the
countercurrent flow and the cocurrent subcritica1 and supercriti
ca1 modes. For details of the experimental procedure, reference
is made to Section 5.2.3.3.
Comparison of Figures 6.19-6.22 shows clearly the varying
sludge thickening performances under the different flow conditions
with the initial feed concentration of 0.5 percent solids by
volume. From a design standpoint, two significant findings are
evident and they are listed below for the convenience of
discussion:
a) that compared to the countercurrent flow (Figure 6.19), the
cocurrent subcritica1 and supercritica1 modes (Figures 6.20
and 6.21) seem to produce a more consistent 'steady-state'
solids underf10w concentration over the entire range of
inclination angles (a) from 20 to 70 degrees.
In the case of the countercurrent flow, the pronounced
fluctuation in Cu arises because of intermittent sludge
discharge along the lower inclined surfaces. The latter is
induced by the additional forces of resistance imposed on
the sludge layer by the actual feed stream acting in the
opposite direction. Because the predominant mechanism of
sludge transport is due to layer movement, it is believed
that at any position along the sludge layer there is a time
1ag between successive intermittent sludge discharge during
184
FIGURE 6.19: EFFECT OF INCLINATION ANGLE ON THE CONSISTENCY OF THE
Svr.1bol - -a
0
x
~
0
Solids cone.
3.5
3.0
2.5
2.0
1.5
1.0
0.5
SOLIDS cOiICENTRATlON IN TRE UNDERFlOW STREAII FOR COUNTERCURRENT nor! ImH THE INITIAL FEED CONCENTRATION. Co ~ 0.5% v/v
Inclination angle et e Separator dimensions:
70° 20°
60° 30° L ~ 56 cm; b ~ 3.4 e[.1;
\I ~ 4 cr.1
45° 45°
30° 60°
20° 700
(% v/v) in underflovl stream. Cu
O~~~~~ __ L--L __ L--L __ L--L __ L--L __ ~~
o 20 40 60 30 100 120 140 1 SO 180 200 220 240 250
Operating Time (mins)
185
FIGURE 6.20: EFFECT OF INCLINATlO1i ANGLE ON THE COr~SISTENCY OF THE SOLI9S CONCENTRATION IN THE UNDERFLo\j STREAM FO~ THE COCURRENT--SUBCRITICAL MODE WITH THE INITIAL FEED CONCENTRATION, Co 0.5% v/v
Symbol Inclination angle Cl 8 Separator dimensions:
A 700 200 L = 66 cm;
600 300 ~J = 4 em 0
)( 45° 45°
• 30° 30°
• Solids cone. (% v/v) in underflol1 stream, eu 3.5
3.0
2.5
b = 3.4 em;
OL-~~~~ __ ~~~~~~~~~~~~ o 20 40 50 30 100 120 140 150 180 200 200
Operating Time (mins)
186
..
FIGURE 6.21: EFFECT OF INCLINATION ANGLE ON THE CONSISTENCY OF THE SOLIDS COt~CEIHRATloN IN THE UtlDERFLOW STREAM FOR THE COCURRENT-SUPERCRITICAL MODE WITH TRE INITIAL FEED CONCENTRATIO~, Co = 5% v/v
Symbol Inclination an91e Cl e
A 700 200 Separator dimensions
0 500 ~Oo ". L = 66 cm;
)( 450 450 W = 4 cm
• 300 600
Solids conc. (% v/v) in underf1o~1 strear.1, Cu 3.5
3.0
2.5
2.0
1.5
1.0
05
b = 3.4 cm;
OL-~~--J-~ __ ~~ __ ~~ __ ~-L __ L-~~. o 20 40 60 80 100 120 140 160 180 200 220 240 260
Operating Time (r.1ins)
137
FIGURE 6.22: EFFECT OF INCLINATION ANGLE ON THE AVERAGE "STEADY-STATE" ..
o
o
SOLIDS CONCENTRATION IN THE UNDERFLOW STREAM FOR THE DIFFERENT FLOW pATTERNS HITH Co - 3.5% v/v
Separator dimensions:
L = 66 cm; b = 3.4 cm; W = 4 cm
Cocurrent-su~ercritical mode
Cocurrent-subcritical mode
Countercurrent flow
Average "steady-state" solids conc. in the underf10w (% v/v) 3.0
2.5
2.0
1.5
1.0
0.5
188
whi ch the sludge layer accumulates suffi cient gravi tati ona 1
mass to overcome the additional viscous resistance imposed
by the countercurrent stream. The cocurrent flow, on the
other hand, by virtue of its sameness of flow direction
actually reinforces the sludge transport, thus producing
a smoother discharge. This explains the greater consis
tency in cu'
From the present results, the use of a countercurrent flow
is therefore to be avoided in situations where a high consis
tency in cu is demanded. For such a requirement, either the
cocurrent subcritical or supercritical mode should be used
instead. However, the overriding "consideration for the
choice between the two is the actual achievable solids con-
centration, cu' in the underflow stream. This will be the
next subject of discussion.
bi} That between the inclination angles (a) of 300 and 550*, the
supercritical mode gives considerably higher average 'steady
state' underflow concentrations than the other two operating
modes. Moreover, its concentration versus a curve, as shown
in Figure 6.22, passes through a maximum at an approximate
optimum inclination angle of 450 - the existence of which has
been predicted during the earlier discussion. The ability to
achieve underflow concentration at a lower inclination angle
is another proof that the supercritical mode is a more superior
* . This range covers the angle requirements of most commercial app1ications11 ,45
189
design for lamella separators.
bi i) A rather unexpected outcome is that at angles greater than
a = 550, the performance curve reverses in favour of the
countercurrent flow giving higher cu• Nevertheless, it
should be noted that on the whole this is not in any way
a disadvantage of the cocurrent supercritica1 mode because
similar underf10w concentrations are also achievable with
the latter, but, at much lower a~gles.
For completeness, explanations to account for the differences
between the concentration profiles of the 3 flow patterns will now
be presented. The subcritica1 and the supercritica1 modes will
first be discussed and a subsequent comparison made with the counter
current flow in an attempt to explain their apparent differences.
As illustrated below, the underf10w concentration profiles for
the first two cases depict 3 performance regimes:
Underf10w concentration, Cu (% v/v)
©
Increasing inclination angle, aO
* This range covers the angle requirements of most commercial app1icationsll ,45
190
The initial increase in Cu along A, up to the optimum point,
is brought about by an increase in the gravitational accelera-
tion that enhances the layer movement responsible for the sludge
flow. However, going beyond the optimum inclination angle, i.e. ~ .
along B, thoughAincreases further the gravitational accelera-
tion actually results in a drop in Cu because of substantial
reduction in the number of layers of solids formed on the lower
inclined surfaces. The latter-results from a consequent reduc
tion in the solids handling capacity of the separator as a
increases. For both the subcritical and supercritical modes,
this optimum angle is approximately 450, though the actual
maximum underflow concentration that is achieved with the latter
is greater by about 34 percent. There are essentially two reasons
for this difference in faY our of the supercritical mode:
i) its higher solids handling capacity, and
ii) the relatively small thickness of its feed stream which
exerts a stronger positive influence on the sludge flow because
of its closer proximity to the sludge layer.
Finally, the upturn along C occurs because all the solids now
have sufficient gravitational acceleration to move spontaneously.
It is believed that at this stage the mechanism of sludge flow has
reverted from layer movement to the bulk movement (refer Section
6.2.1).
By comparison the underflow concentration profile for the
countercurrent flow is completely different - in this case, Cu
191
shows a consistent increase with increasing inclination angle.
It appears that the additional resistance to sludge flow, provi
ded by the feed stream, has 'ironed' out the occurrence of
optimum conditions created by the varying degree of layer move
ment at different inclination angles and which characterise the
subcritica1 and supercritical modes of operation. Because of
the additional resistance to flow and its lower solids handling
capacity, the countercurrent flow operation - between the incli
nation angles (a) of 30 and 55 degrees - is shown to produce
much lower underflow concentrations than the supercritica1 mode.
For example, to achieve the same maximum Cu obtained with the
supercritical mode at 450, the countercurrent flow will have to
be operated at approximately 70 degrees. This means a reduction
to the total projected settling area of about 50% - once again
indicating the vast potential improvement that can be made to the
current commercial design using the supercritical mode.
However, why the countercurrent flow should produce better
sludge thickening performances above the inclination angle (a) of
55 degrees is, at the moment, not sufficiently well understood.
This finding warrants further investigation.
The effect of feed concentration on the performance of sludge
thickening is shown by the results in Figures 6.23-6.26 for
Co = 2% v/v. Clearly, by contrast with the previous case
(i.e. Co = 0.5% v/v), the consistency of the achievable underflow
concentration is equally good for the three different modes of
192
FIGURE 6.23: EFFECT OF INCLINATION ANGLE ON THE CONSISTENCY OF THE SOLIDS CONCENTRATION IN THE DNDERFLOW sTREAf1 FOR COON1 ER CURRENT FLOW WITH THE INITIAL FEED CONCENTRATION, Co - 2.0% v/v
Separator dimensions: .
L = 66 cm; b = 3.4 cm; H = 4 cm
Solids conc. (% v/v) in underflow stream, Cu 8.5
8.0
7.0
6.0
Symbol Inclination Angle
" e
5.0 A 700 200
c 600 300
4.0 x 450 450
0 300 300
3.0
2.0
1.0
o L-____ ~ ____ -L ____ ~L-____ ~ ____ _L ____ ~
o 20 40 60 80 100 120 Operating Time (mins)
193
FIGURE 6.24: EFFECT OF INCLINATION ANGLE ON THE CONSISTENCY OF THE "SOLIDS CONCENTRATION IN TRE UNDERFLOH STREAM FOR THE COCURRENT -SUBCRITICAL tlODE UITH THE INITIAL FEED CONCENTRATION, Co - 2.0% v/v
Separator dimensions: L = 66 cm; b = 3.4 cm; W = 4 cm
Solids conc. (% v/v) in underflo~1 stream, Cu 8.5
8
7
6
Symbol Inclination Angle
" e 5
c. 700 200
4 [J 600 300
x 450 450
3 0 300 600
1 .
o o 20 40 60 SO 100
Operating Time (mins)
194
120
FIGURE 6.25: EFFECT OF INCLINATION ANGLE ON THE CONSISTENCY OF SOLIDS CONCENTRATION IN THE UNDERFLOVl STREAf1 FOR THE COCURRENTSUPERCRITICAL flODE HITH THE INITIAL FEED CONCENIRATIoN, c = 2% v/v 0--';":""';-
Separator dimensions: .11
L = 66 cm; b = 3.4 crn; W = 4 cm
Solids conc. (% v/v) in underflOl'/ stream, Cu 8.5
8
7
6 Symbol Inclination Angle
" e
5 Il. 70° 200
0 60° 300
4 X 45° 45°
0 30° 300
3
2
1
o o 20 40 60
Operating Time (mins)
195
o
FIGURE 6.26: EFFECT OF INCLINATION ANGLE ON THE AVERAGE "STEADY-STATE" SOLIDS CDrICENTRATION IN THE UNDERFLO\~ STREAr! FOR THE DIFFERENT FLOIj PATTERNS WITH Co = 2% v/v
Separator dimensions:
L = 66 cm; b = 3.4 cm; W = 4 cm
Average "steady-state" solids concentration in the underf10w (% v/v)
8.5
8.0
7.5
7.0
6.5
6.0
5.5
5.0
ot I I
200 30° 40°
700 60° 500
196
C Cocurrent-supercriti ca 1 mode
Cocurrent-subcritica1 mode "6.
o Countercurrent flow
I I I I
500 600 70° 80° (,,0)
400 300 20° 100 (e)
operation. The reason being that at such a high feed concen
tration, the effective increase in the solids loading to the
separator, results in the sludge movement becoming predominantly
gravity controlled. As such the influence of different flow
patterns on the sludge transport becomes masked by the gravita
tional effects on the layer movement. For the same reason, the
concentration profiles (Figure 6.26) merely shows an upward
• trend without exhibiting any maximum or minimum turning points.
Interesti ng1y, the countercurrent fl ow once agai n see",,,, to
produce generally higher average "steady-state" underflow con
centrations than both the subcritica1 and supercritica1 modes.
Unfortunately no satisfactory explanation has been found to
account for this result.
The very changeable trend in the. sludge thickening performance
clearly underlines the urgent need for a mathematical model to
describe the sludge transport behaviour along the lower inclined
surfaces. Only from that can reliable design guidelines be formu
lised. Nevertheless, the present findings are significant in
highlighting the vast potential improvement that can be made,
particularly in adopting the supercritical mode of operation.
Moreover, a useful foundation for the development of a mathema
tical model to describe the sludge flow is provided by the results
in Section 6.2.1.
197
CHAPTER 7
CONCLUSIONS
7.1 The behaviour of inclined sedimentation in both the low and
high aspect ratio vessels can be accurately described by the
Acrivos and Herbolzheimer models under the following sets of
conditions:
Low aspect ratio case: h 1.13 < b < 3.42
1% v/v < c < 30% v/v o 200
< a < 700
7.61 X 104 < Ao< '8.48 X 107
0.17 <R<2.12 o
High aspect ratio case: 41.31 < ~ < 75
1% v/v < c < 2~% v/v o 200
< a < 450
4.33 x 108 > Ao> 5.47 X 106
3.88 < Ro< 10.76
•
The latter can therefore be used as means for predicting and
interpreting the overall settling behaviour in both batch and
continuous lamella separators.
198
7.2 For inclined sedimentation in a high aspect ratio separator,
i.e. h/b =0(102), the essential steady-state conditions are
not .inherently attainable. There may be constraints on the
dimensions and design of the separator that need to be
satisfied before steady-state can be achieved.
As aO design guideline, the following constraint on the
channel spacing for the lamella separator can be used:
i . e. 192 tanS V \l X . 0
7.3 Layer movement is the predominant mechanism by which sludge
is transported down the lower inclined surfaces of a
lamella separator. Some of the relevant parameters of layer
movement that should form a useful basis for a mathematical
model are:
Size of the sludge solids,
Density of the sludge solids,
Shape and surface texture of the sludge soiids, and
Liquid viscosity.
7.4 It is evident that, under certain operating conditions, it is
possible to optimise the lamella separator design by working
at an optimum inclination angle, i.e. that which gives the
desired level of sludge thickening at the maximum separator
throughput. In our experiments with the initial feed
199
•
concentration of 0.5 percent solids by volume, such an
optimum inclination angle (approximately 45°) exists for
both the cocurrent subcritical and supercritical modes of
operation. However, the actual maximum underflow concen
tration that is achieved with the latter is greater by
about 35 percent, hence sho~ling itself as being of a
superior design •
7.5 Owing to the potential problems of particle re-entrainment:
caused mainly by flow instability, there exists an optimum
aspect ratio for a lamella separator beyond which the design
becomes uneconomic. This is because of the diminishing return
in the achievable maximum overflow rates. Such an optimum
- as defined by the uppermost limiting value, (h/b)UL - is
given belo~1 for the cases in which the initial feed concen
tration is 0.5 and 2 percent solids by volume; and the
separator channel spacing is 3.4 cm.
Co (% v/v)
0.5
2.0
(h/b)UL
25-30
15-22.5
Clearly, a lower limiting aspect ratio is imposed on the
second case because of the potentially more pronounced
effects of flow instability. The design strategy, therefore,
is to provide shorter and broader settling channels when
treating suspensions of higher concentrations.
200
7.6 The Nakamura and Kuroda equation is shown to be capable
of predicting very accurately the maximum overflow rate
of a lamella separator. This is on the precondition that
7.6.1 the requirements for achieving the essential steady-
state conditions are met, and
7.6.2 the dimensions of the separator are suitably chosen
to obviate the adverse effects of flow instability,
which lead to the re-entrainment of particles into
the overflow.
7.7 The cocurrent supercritical mode of operation is shown to
be far superior. to both the subcritical mode and the counter
current fl O~I for the following reasons:
7.7.1 It is inherently a more stable system, and hence
reduces drastically the potential problems of particle
re-entrainment. As a result, its maximum achievable
overflow rates are often attainable, as testified by
the current experimental results.
7.7.2 In general it gives better sludge thickening performan
ces for two reasons:
7.7.2.1 Greater consistency in the underflow solids
concentration, and
7.7.2.2 The attainment of relatively high underflow
concentrations at lower inclination angles (al,
i.e. higher overall separator throughput.
201
•
CHAPTER 8
RECOMMENDATIONS FOR FURTHER WORK
Outlined below are some of the topics, which in the author's
opinion, warrant further investigation. It should, however, be
stressed that these recommendations are additional to those already
made under the relevant sections in the thesis.
8.1 All the solid-liquid systems that have been used in the
experiments in this thesis are fully dispersed in nature.
Hence, the various design guidelines that have been derived
from the present research findings are strictly applicable
only to such systems. It is suggested, therefore, that
alongside the proposed further experiments using the fully
dispersed systems. similar analyses be made on 'real' suspen
sions. The latter will include f10ccu1ated suspensions and
sludges of deformable particles.
Only then, perhaps, can more general guidelines be established.
8.2 Present experimental evidence shows the Acrivos and Herbo1zheimer's
model to be capable of adequately describing the velocity field
in the clear liquid layer that is formed beneath the upper
inclined surface. It is therefore justified to use the predic-
ted velocity field in the development of a stability analysis to
define the initiating conditions responsible for flow instabi··
1ity. The latter should provide the means for determining the
202
optimum separator aspect ratio which will contribute towards
the development of an optimisation procedure for the lamella
separator design.
8.3 It is proposed that the continuum mechanics approach that has
been undertaken by Acrivos and Herbolzheimer to model the
inclined sedimentation process in a two-dimensional settling
channel be extended to a three-dimensional one. Such a model
will enable the investigation of different plate configurations
on the performance of a lamella separator. It is believed that
the parallel plate configuration that is commonly used in
existing commercial units is not the optimum4
i
203
APPENDICES
A.1 EXPERIMENTAL VERIFICATION OF BATCH INCLINED SEDIMENTATION MODELS
A.1.1 Experimental conditions
A.1.2 Experimental verification of inclined sedimentation models by Acrivos and Herbo1zheimer
A.1.2.1 Low aspect ratio case
A.1.2.2 High. aspect ratio case
A.1.3 Experimental verification of inclined sedimentation models by Nakamura and Kuroda
Tables A.1-A.15
Experimental verification of predicted steady-state clear liquid layer thick-
Page No.
206
206
207
207
208
209
ness (Low aspect ratio case) 212
Tables A.16-A.27
Experimental verification of predicted velocity field in the clear liquid layer (Low aspect ratio case) 227
Tables A.28-A.36
Experimental verification of predicted steady-state clear liquid layer thick-ness (High aspect ratio case) 239
A.2 OPERATING PERFORMANCE OF THE CONTINUOUS LAMELLA SEPARATOR .. , 248
A.2.1 Experimental conditions 248
A.2.2 Maximum handling capacity for the pure clear liquid overflow 249
204
Page No.
Tables A.37-A.44
Maximum overflow rates for the different modes of operation 249
A.2.3 Sludge thickening performance 257
Tables A.45-A.69
Solids concentration in the underflow.(sludge) stream as a function of the operating time for the different modes of operation
205 .
APPENDIX A.1
A.1 EXPERIMENTAL VERIFICATION OF BATCH INCLINED SEDIMENTATION MODELS
A.1.1 Experimental Conditions
Details of suspension
Glass beads:
Size range = 90-125 ~m (spherical)
Particle density = 2460 kgm- 3
Suspension liquid:
*Reofos 65 (25.5% v/v) and Reomo1 DBP (74.5% v/v)
Liquid density @ 250 C = 1079.5 kgm- 3
Liquid viscosity @ 25 0C = (22.2528 x 10- 3 ) Nsm-2
Verti ca1 batch sett1 ing velocity of suspensi on:
Concentration of particles Vertical batch settling in suspension, v/v velocity (v ) cm/s
, 0
0.01 2.55 x 10-2
0.025 2.03 x 10-2
0.05 1.67 x 10-2
0.10 1 .48 X 10-2
0.15 1.16 x 10-2
0.20 0.99 x 10-2
0.30 0.63 x 10-2
.
* Manufacturer: Ciba-Geigy.
206
A.l.2 Experimental Verification of Inclined Sedimentation ~'odels by Acrlvos and Rerbolzhelmer
A.l.2.1 Low aspect ratio case
The theoretical predictions for the steady-state thickness of
the clear liquid layer that is formed beneath the upper inclined sur
face and the velocity field in the clear liquid layer itself have
been verified experimentally. The respective predictive equations
are given below:
Le
and
?; = (3 X: tane)1/3
'" U = Cose en - ,y2) Eqn. 4.16
Eqn. 4.12
However, for the actual calculation purposes, Equations (4.12) and
(4.16) have been rewritten in terms of the dimensional variables
as:
_3_X rt_a_n_e_v...;o::..,-ll )y., oD = ( ~
g (p p - p) Co and
_ y2/2}
The nomenclature used in the equations above is the same as that
used throughout the thesis.
207
A.l.2.2 High Aspect Ratio Case
In contrast \~ith the low aspect ratio case, the existence of
a critical point of discontinuity in the clear liquid/suspension
interface under certain settling conditions has been verified experi
mentally with the use of Equation 4.18. The latter, expressed in
terms of the dimensional variables, is given by:
b3g (p - p) c p 0
192 tane Vo 11
In accordance with the theoretical predictions, a steady-state clear
liquid/suspension interface is attainable only below Xc - above
that critical point of discontinuity, the interface will be in
perpetual transience (details already given in Section 4.2.1). The
steady-state clear liquid layer thickness below the point of dis
continuity has also been verified experimentally with the use of
the dimensional form of Equation 4.17,
i.e.
where x " xc'
208
, ..
A.1.3 Experimental Verification of Inclined Sedimentation Model oy Nakamura and Kuroda
The Nakamura and Kuroda equation has been tested to establish.
the approximate range of conditions under which it can be accurately
used to predict the initial rate of inclined sedimentation in a
batch separator. The principal objective is to obtain some realistic
orders of magnitude of A and R, which according to theory2,3 should
be asymptotically large and negligibly small respectively. In the
present analysis the initial rate of inclined sedimentation is
expressed in terms of the initial rate of clear liquid generated
per unit width of the separator, and accordingly the following modi
fied Nakamura and Kuroda equation has been used:
= v (1 + h Sina) b o b Cos a
where q = volumetric rate of clear liquid generated per unit width
of the separator,
(~~)N-K = the rate of fall of the top horizontal clear liquid/
suspension interface given by the Nakamura and Kuroda
equation, and
209
Wid h
------, --------=- = ~ .=-..=-
+ + + + dh at ____ Jt
Vo = vertical batch settling velocity of suspension at Co (the
actual experimental values ar.e used and these are given
in A.lol).
On the other hand, the experimental value for q is obtained
from a plot of the vertical area (A)* of the clear liquid layer that
is formed as a function of time by taking the appropriate slope,
~, at the required time t - see illustrations below.
Clear liquid layer
t=O
Width Suspension layer
A = Vertical area of clear liquid layer at time t
Area of clear liquid layer, A
t Settling time, t
* To obtain the actual volume this ver.t'i.cal area must be multipled by the wi dth (a constant).
The essential experimental data for the above area-time plot is
obtained from the cine-film of the entire settling process using
the Vanguard machine.
TABLE A.l
EXPERIMENTAL VERIFICATION OF PREDICTED STEADY-STATE CLEAR LIQUID LAYER THICKNESS
Low Aspect Ratio Case
1.13 Aspect ratio (ho/b)
Angle of inclination,s
Initial concentration of suspension, Co
600 (from the vertical)
Ratio of sedimentation Grashof number to sedimentation Reynolds number, 11.0
Sedimentation Reynolds number, Ro
Position along Predicted thick-upper inclined ness of clear surface, x(cm) liquid layer,
oD (mm)
1 1.30 2 1.63 3 1.87 4 2.06 5 2.22 6 2.36 7 2.48 8 2.59 . 9 2.70
10 2.79
212
1% v/v
7.61 x 10"
0.70
Measured thick- Predicted thickness ness of clear ~leasured thlckness liquid layer,
(oD)m' mm
1.54 0.84 1.67 0.98 1.79 1.04 2.05 1.00 2.20 1.01 2.44 0.97 2.56 0.97 2.77 0.94 3.08 0.88 3.13 0.89
TABLE A.2
EXPERIMENTAL VERIFICATION OF PREDICTED STEADY-STATE CLEAR LIQUID LAYER THICKNESS
Low Aspect Ratio Case
Aspect Ratio, h/b 1.13 e 600
Co 5% v/V A
.• 0 5.82 x 105
Ro 0.46
Position along Predicted thick- Measured thick- Predicted thickness upper inc1 tned ness of clear ness of clear f·1easured thlckness surface, x(cm) liquid layer,
0D (mm) liquid layer,
(oD)m' mm
1 0.66 0.67 0.99 2 0.83 0.80 1.04 3 0.95 0.93 1.02 4 1.05 1.07 0.98 5 1.13 1.15 0.98 6 1.20 1.20 1.00 7 1.26 1.32 0.96 8 1.32 1.32 1.00 9 1.37 1.45 0.95
213
TABLE A.3
EXPERIMENTAL VERIFICATION OF PREDICTED STEADY-STATE
CLEAR LIQUID LAYER THICKNESS
Low Aspect Ratio Case
Aspect Ratio, ho/b e
:
1.13 600
10% v/v 1.31 x 106
0.41
Position along Predicted thick- Measured thick- Predicted thickness upper inclined ness of cl ear ness of clear Measured thi ckness surface, x(mm) 1 iquid layer,
0D (mm) liquid layer,
(oD)m' mm
1 0.50 0.53 0.94 2 0.63 0.66 0.96 3 0.72 0.68 1.06 4 0.80 0.79 1.01 5 0.86 0.84 1.02 6 0.91 1.05 0.87 7 0.96 1.05 0.91 8 1.00 1.05 0.95
TABLE A.4
EXPERIMENTAL VERIFICATION OF PREDICTED STEADY-STATE
CLEAR LIQUID LAYER THICKNESS
Low Aspect Ratio Case
Aspect ratio, ho/b e
:
:
1.13 600
20% v/v 3.92 x 106
0.27
Position along Predicted thick- Measured thick- Predicted thickness upper incl ined ness of clear ness of clear Measured thickness surface, x(mm) liquid layer,
0D (mm) liquid layer,
(oD)m' mm
1 0.35 0.41 0.85 2 0.44 0.43 1.02 3 0.50 0.54 0.93 4 0.55 0.59 0.93 5 0.60 0.63 0.95
6 0.63 0.67 0.95
7 0.67 0.73 0.92 8 0.70 0.74 0.95 9 0.72 0.77 0.94
10 0.75 0.84 0.89
215
TABLE A.5
EXPERIHENTAL VERIFICATION OF PREDICTED STEADY-STATE
CLEAR LIQUID LAYER THICKNESS
Low Aspect Ratio Case
Aspect Ratio, ho/b e
:
:
1.13
600
30% v/v 9.24 x 106
0.17
Position along Predicted thick- Measured thi ck- Predicted thickness upper inclined ness of clear ness of clear Measured thlckness surface, x(an) liquid layer, li(Uid layer
8D (mm) 0D)m' mm
1 0.26 0.19 1.37
2 0.33 0.32 1.03
3 0.38 0.40 0.95
4 0.42 0.46 0.91
5 0.45 0.49 0.92
6 0.48 0.54 0.89
7 0.50 0.56 0.89
8 0.52 0.58 0.90
9 0.54 0.59 0.92
216
TABLE A.6
EXPERIMENTAL VERIFICATION OF PREDICTED STEADY-STATE fLEAR LIQUID LAYER THICKNESS
Low Aspect Ratio Case
Aspect Ratio, ho/b : 3.42 e : 200
c : 1% v/v 0
6.97 x 105 11 : 0
Ro : 2.12
Position along Predicted thick- t~easured thick- Predicted thickness upper inclined ness of clear ness of clear Measured thlckness surface, x(cm) liquid layer liquid layer
"D (mm) (oD)m' mm
1 0.77 0.82 0.94 2 0.97 1.01 0.96 3 1.11 1.09 1.02 4 I 1.22 1.23 0.99 5 1.32 1.35 0.98 6 1.40 1.49 0.94 7 1.47 1.55 0.95 8 1.54 1.64 0.94. 9 1.60 1.72 0.93
10 1.66 1.77 0.94 11 1. 71 1.89 0.91 12 1. 76 1.95 0.90 13 1.81 2.16 0.84 14 1.85 2.22 0.83 15 1.90 2.43 0.78 16 1.94 2.65 0.73
217
TABLE A.7
EXPERIMENTAL VERIFICATION OF PREDICTED STEADY-STATE CLEAR LIQUID LAYER THICKNESS
Low Aspect Ratio Case
Aspect Ratio, ho/b a
: 3.42 200
5% v/v 5.32 x 106
1.39
Position along Predicted thick- Measured thi ck- Predi cted thi ckness upper incl ined ness of clear ness of clear ~leasured thl ckness surface, x(cm) liquid layer, liquid layer,
50 (mm) (5 D)m' mm
1 0.39 0.54 0.72 2 0.49 0.57 0.86 3 0.56 0.59 0.95 4 0.62 0.62 1.00 5 0.67 0.65 1.03 6 0.71 0.70 1.01 7 0.75 0.81 0.93 8 0.78 0.92 0.85 9 0.81 . 1.05 0.77
10 0.84 1.08 0.78 11 0.87 1.08 0.81 12 0.90 1.11 0.81 13 0.92 1.14 0.81 14 0.94 1.19 0.79 15 0.97 1.22 0.80 16 0.99 1.22 0.81
218
TABLE A.8
EXPERIMENTAL VERIFICATION OF PREDICTED STEADY-STATE CLEAR LIQUID LAYER THICKNESS
Low Aspect Ratio Case
Aspect Ratio, ho/b 3.42 e 200
Co : 10% v/v
Ao : 1.20 x 107
Ro : 1.23 ...
Position along Predicted thick- Measured thick- Predi cted thi ckness upper inclined ness of clear ness of clear Measured thlckness surface, x(cm) liquid layer liquid layer,
0D (mm) (oD)m' mm
1 0.30 - -2 0.38 0.43 0.88 3 0.43 0.49 0.88 4 0.47 0.51 0.92 5 0.51 0.54 0.94 6 0.54 0.54 1.00 7 0.57 0.59 0.97 8 0.60 0.59 1.02
9 0.62 0.65 0.95
10 0.64 0.70 0.91
11 0.66 0.76 0.87 12 0.68 0.81 0.84
13 0.70 0.86 0.81
14 0.72 0.97 0.74
15 0.74 . 1.03 0.72
16 0.75 1.03 0.73
219
TABLE A.9
EXPERIMENTAL VERIFICATION OF PREDICTED STEADY-STATE
~LEAR LIQUID LAYER THICKNESS
Lo\~ Aspect Rati 0 Case
Aspect Ratio, ho/b a
Co
Ao Ro
3.42
200
20% v/v 3.59 x 107
0.82
Position along Predi cted thi ck- Measured thi ck- Predicted thickness upper inclined ness of clear ness of clear Measured thl ckness surface, x(cm) liquid layer, liquid layer,
0D (mm) (oD)m' mm
1 0.21 - -2 0.26 0.32 0.81 3 0.30 ·0.36 0.83 4 0.33 0.40 0.83 5 0.35 0.43 0.81 6 0.38 0.46 0.83 7 0.40 0.47 0.85 8 0.41 0.48 0.85 9 0.43 0.50 0.86
10 0.45 0.51 0.88
11 0.46 0.53 0.90 12 0.47 0.54 0.87
13 0.49 0.56 0.88
14 0.50 0.59 0.85
15 0.51 0.62 0.82
16 0.52 0.65 0.80
17 0.53 0.67 0.79
220
TABLE A.10
EXPERIMENTAL VERIFICATION OF PREDICTED STEADY-STATE CLEAR LIQUID LAYER THICKNESS
Low Aspect Ratio Case
Aspect R~tio, h/b a
3.42 200
30% v/v 8.47 x 101
0.52
Position along Predicted thick- Measured thi ck- Predicted thickness upper inclined ness of clear ness of clear Measured thlckness surface, x(cm) liquid layer, liquid layer,
oD (mm) (oD)m' mm
1 0.16 - -2 0.20 - -3 0.22 - -4 0.25 - -5 0.27 - -6 0.28 0.23 1.22 7 0.30 0.27 loll 8 0.31 0.31 1.00 9 0.32 0.35 0.91
10 0.34 0.38 0.90 11 0.35 0.40 0.88 12 0.36 0.41 0.88 13 0.37 0.43 0.86 14 0.38 0.45 0.84 15 0.38 0.48 0.79 16 0.39 0.48 0.81 17 0.40 0.51 0.78
221
TABLE A.11
EXPERIMENTAL VERIFICATION OF PREDICTED STEADY-STATE CLEAR LIQUID LAYER THICKNESS
Low Aspect Ratio Case
Aspect Ratio. ho/b 3.42 e 300
: 1% v/v 6.97 x 105
2.12
Position along Predicted thick- Measured th i ck- Predicted thickness upper inclined ness of clear ness of clear Measured thlckness surface. x(cm) liquid layer.
cD (mm) 1 i q ui d 1 aye r •
(cD)m' mm
1 0.90 - -2 1.13 - -3 1.30 1.83 0.71 4 1.43 1.89 0.76
5 1.54 2.01 0.77
6 1.63 2.07 0.79 7 1. 72 2.13 0.81
8 1.80 2.20 0.82
9 1.87 2.26 0.83
10 1.94 2.32 0.84
11 2.00 2.43 0.82
12 2.06 2.44 0.84
13 2.11 2.44 0.87
14 2.17 2.49 0.87
15 - 2.22 2.49 0.89
16 2.27 2.56 0.89
17 2.31 2.56 0.90
222
TABLE A.12
EXPERIMENTAL VERIFICATION OF PREDICTED STEADY-STATE CLEAR LIQUID LAYER THICKNESS
Low Aspect Ratio Case
Aspect Ratio, ho/b e :
:
3.42 300
5% v/V 5.32 x 106
1.39
.
Pos iti on along Predicted thick- r1easured thi ck- Predicted thickness upper inclined ness of clear ness of clear Measured thl ckness surface, x(cm) liquid layer,
oD (mm) 1 iquid layer,
(oD)m' mm
1 0.46 - -2 0.58 - -3 0.66 0.68 0.97 4 0.72 0.81 0.89 5 0.78 0.87 0.90 6 0.83 0.93 0.89 7 0.87 0.99 0.88 8 0.91 1.09 0.84 9 0.95 1.12 0.85
10 0.98 1.18 0.83 11 1.01 1.18 0.86 12 1.05 1.22 0.86 13 1.07 1.24 0.86 14 1.10 1.26 0.87 15 1.13· 1.28 0.88 16 1.15 1.30 0.89
17 1.17 1.33 0.88 18 1.20 1.35 0.89
??1
TABLE A.13
EXPERIMENTAL VERIFICATION OF PREDICTED STEADY-STATE CLEAR LIQUID LAYER THICKNESS
Low Aspect Ratio Case
Aspect Ratio, ho/b 3.42 a 300
c 10% v/v 0
1\0 1.20 x 107
Ro 1. 23
Position along Predi cted tili ck- Measured thick- Predicted thickness upper inclined ness of clear ness of clear Measured thlckness surface, x(cm) liquid layer,
oD (mm) liquid layer,
(oD)m' mm
1 0.35 - -2 0.44 - -3 0.50 0.55 0.91 4 0.56 0.57 0.95 5 0.60 0.63 0.95 6 0.63 0.68 0.93 7 0.67 0.73 0.92 8 0.70 0.77 0.91 9 0.72 0.77 0.94
10 0.75 0.79 0.95 11 0.77 0.82 0.94 12 0.80 0.82 0.98 13 0.82 0.84 0.98 14 0.84 0.86 0.98 15 0.86 0.90 0.96 16 0.88 0.93 0.95
17 0.89 1.05 0.85 18 0.91 1.11 0.82
224
,
TABLE A.14
EXPERIMENTAL VERIFICATION OF PREDICTED STEADY-STATE CLEAR LIQUID LAYER THICKNESS
Low Aspect Ratio Case
Aspect Ratio, h/b 3.42 e : 300
c' 30% v/V 0
110 3.59 X 107
.. Ro 0.82
Position along Predicted thick- Measured thick- Predicted thickness upper inclined ness of clear ness of clear Measured thl ckness surface, x(cm) liquid layer,
0D (mm) liquid layer
(oD)m' mm
1 0.24 0.25 0.96
2 0.30 0.31 0.97
3 0.35 0.31 1.13
4 0.38 0.38 1.00
5 0.41 0.47 0.87
6 0.44 0.50 0.88
7 0.46 0.56 0.82
8 0.48 0.56 0.86
9 0.50 0.59 0.85
10 0.52 0.59 0.88
11 0.54 0.59 0.92
12 0.55 0.63 0.87
13 0.57 0.63 0.91
14 0.58 0.63 0.92
15 0.60 0.65 0.92
16 0.61 0.66 0.92
17 0.62 0.66 0.94
18 0.63 0.69 0.91
225
TABLE A.15
EXPERIMENTAL VERIFICATION OF PREDICTED STEADY-STATE CLEAR LIQUID LAYER THICKNESS
Low Aspect Ratio Case
Aspect Ra ti 0, ho/b 3.42 e 300
Co 30% v/V
Ao 8.47 x 107
.-. Ro 0.52
Position along Predicted thick- Measured thick- Predicted thickness upper i nc 1 i ned ness of clear ness of clear Measured thlckness surface, x(cm) liquid layer,
cS D (mm) liquid layer
(oD)m' mm
1 0.18 - -2 0.23 - -3 0.26 - -4 0.29 - -5 0.31 - -6 0.33 - -7 0.35 - -8 0.36 0.32 1.13 9 0.38 0.34 1.12
10 0.39 0.34 1.15 11 0.40 0.39 1.03
12 0.42 0.42 1.00 13 0.43 0.46 0.94 14 0.44 0.48 0.92 15 0.45 0.51 0.88 16 0.46 0.51 0.90 17 0.47 0.54 0.87 18 0.48 0.54 0.89
226
TABLE A.16
EXPERIMENTAL VERIFICATION OF PREDICTED VELOCITY FIELD IN THE CLEAR LIQUID LAYER
Low Aspect Ratio Case
Aspect Ratio, ho/b : 1.80 e : 450
c 1% v/v 0
Ao : 1.93xlOs
Ro 1.13
ILocation of measurement }Osrtlor ~OSltl on Predi cted Predicted Measured along in clear thickness velocity velocity upper 1 iqui d of clear at (x,y) at (x,y) incline( layer liquid surface, normal layer at x (cm) to x X,8D(I11I11) mm S-1 mm s-l
y (mm)
4 0.5 1.71 3.15 3.95 4 1.0 1. 71 5.22 4.62 4 1.5 1. 71 6.23 4.59
6 0.5 1.96 3.68 4.14 6 1.0 1.96 6.29 6.10 6 1.5 1.96 7.82 6.04
8 0.5 2.16 4.11 4.76 8 1.0 2.16 7.14 6.80 8 1.5 2.16 . 9.09 7.44 8 2.0 2.16 9.97 7.32
227
Predicted velocity Measured ve loci ty , . .
0.80 1.13 1.36
0.89 1.0.3 1.29
0.86 1.05 1.22 1.36
TABLE A.17
EXPERIMENTAL VERIFICATION OF PREDICTED VELOCITY FIELD IN THE CLEAR LIQUID LAYER
Low Aspect Ratio Case
Aspect Ratio, h/b 1.80 e 450
c 2~% v/v 0
Ao 6.07 X 105
R • o . 0.89
Location of measurement Posltlon Position Predi cted Predicted Measured along in clear thickness veloci ty velocity upper 1 iqui d of clear at (x ,y) at (x,y)· inclined layer liquid surface, normal layer at x (cm) to x x,oD(mm) mm s-1 mm S-1
y (mm)
4 0.5 1.17 4.95 6.36
6 0.5 1.34 5.86 7.33 6 1.0 1.34 9.03 8.25
8 0.5 1.47 6.58 8.51 8 1.0 1.47 10.48 9.44
228
Predicted velocity Measured velocity
0.78
0.80 1.09
0.77 1.11
TABLE A.1B
EXPERIMENTAL VERIFICATION OF PREDICTED VELOCITY FIELD IN THE CLEAR LIQUID LAYER
Low Aspect Ratio Case
Aspect Ratio, h/b : 1.80 a 450
Co : 5% v/v
Ao 1.47 x 106
Ro : 0.73
Location of measurement Positi on Position Predicted Predi cted Measured along in clear thi ckness velocity velocity upper 1 iqui d of clear at (x,y) at (x,y) inclined layer 1 iqui d surface, normal layer at x (cm) to x x,oD(mm) mm 5-1 mm S-1
y (mm)
4 0.5 0.87 6.67 5.24
6 0.5 0.96 7.63 9.48
8 0.5 1.09 9.10 10.77
229
Predicted velocitl Measured velocity
1.27
0.81
0.85
TABLE A.19
EXPERII-1ENTAL VERIFICATION OF PREDICTED VELOCITY FIELD IN THE CLEAR LIQUID LAYER
Low Aspect Ratio Case
Aspect Ratio, ho/b : e :
Co : A • o • R • o .
3.42 200
1% v/v 6.97 x 105
2.12
Location of measurement P051tlon 1'OS1 t1 on Predicted Predicted Measured along in clear thi ckness velocity velocity upper 1 iquid of clear at (x,y) at (x,y) inclined layer 1 i qui d surface, normal layer at x (cm) to x x'''D(mm) mm S-l mm S-l
y (mm)
4 0.5 1.22 2.78 2.98 4 1.0 1.22 4.14 3.20
8 0.5 1.54 3.69 4.51 8 1.0 1.54 5.95 4.96
12 0.5 1.76 4.33 6.11 12 1.0 1.76 7.23 6.42 12 1.5 1. 76 8.70 6.53
?,"
. .
Predicted velocitl Measured velocity
0.93 1.29
0.82 1.20
0.71 1.13 1.33
..
TABLE A.20
EXPERH1ENTAL VERIFICATION OF PREDICTED VELOCITY FIELD IN THE CLEAR LIQUID LAYER
Low Aspect Ratio Case
Aspect Ratio, \/b: 3.42
a 200
2!% v/v
2.19 x 106
Location of measurement Position Position Predicted Predicted Measured along in clear thickness velocity velocity upper 1 i qui d of clear at (x,y) at (x,y) incl ined layer liquid surface, normal layer at x (cm) to x x,oD(mm) mm S-l mm S-l
y (mm)
4 0.5 0.84 4.18 4.27
8 0.5 1.05 5.74 6.13
8 1.0 1.05 7.90 6.90
12 0.5 1.21 6.83 8.17
12 1.0 1.21 10.08 8.75
231
Predicted velocity Measured veloclty
0.98
0.94
1.14
0.84
1.15
TABLE A.21
EXPERIMENTAL VERIFICATION OF PREDICTED VELOCITY FIELD IN THE CLEAR LIQUID LAYER
Low Aspect Ratio Case
Aspect Ratio, h/b . 3.42
9 200
Co 5% v/v
Ao 5.32 x 106
Ro 1.39
Location of measurement Positi on Position Predicted Predi cted Measured along in clear thickness velocity velocity upper liquid of clear at (x,y) at (x,y) inclined layer li qui d surface, normal layer at x (cm) to x x,oD(mm) mm S-l mm S-l
y (mm)
4 0.5 0.62 5.31 5.22
6 0.5 0.71 6.60 6.51
8 0.5 0.78 7.61 7.82
10 0.5 0.84 8.48 8.74
12 0.5 0.90 9.23 9.59
232
Predicted velocit~ Measured veloclty
1.02
1.01
0.97
0.97
0.96
TABLE A.22
EXPERmENTAL VERIFICATION OF PREDICTED
VELOCITY FIELD IN THE CLEAR LIQUID LAYER
Low Aspect Ratio Case
Aspect Ra ti 0, h/b 3.42
e 300
Co 1% v/v
Ao 6.97 x 105
Ro 2.12
Loca tion of measurement
Position Position Predicted Predicted Heasured along in clear thi ckness velocity velocity upper 1 i qui d of clear at (x,y) at (x,y) inclined layer liquid
. surface, normal layer at x (cm) to x x,oD(mm) mm S-l mm s-l
y (mm)
4 0.5 1.43 3.10 3.75
4 1.0 1.43 4.88 3.97
8 0.5 1.80 4.08 5.36
8 1.0 1.80 6.84 5.84
8 1.5 1.80 8.28 6.17
12 0.5 2.06 4.76 6.84
12 1.0 2.06 8.21 7.38
12 1.5 2.06 10.33 8.10
233
Predicted velocitt f'lea 5 ure d ve 1 oei ty
0.83
1.23
0.76
1.17 1.34
0.70
1.11 1.28
TABLE A.23
EXPERIMENTAL VERIFICATION OF PREDICTED VELOCITY FIELD IN THE CLEAR LIQUID LAYER
Low Aspect Ratio Case
Aspect Ratio, ho/b : e :
c . o • Ao Ro :
3.42 300
2~% v/v 2.19xl06
1.68
Location of measurement
Position Position Predicted Predicted r,leasured along in clear thickness velocity velocity upper 1 i qui d of clear at (x,y) at (x,y) inc1 ined layer liquid surface, normal layer at x (cm) to x x,oD(mm) mm s-l mm 5-1
y (mm)
4 0.5 0.97 4.77 5.19 , 8 0.5 1.23 6.44 7.40 8 1.0 1.23 9.58 8.34
12 0.5 1.41 7.61 9.46 12 1.0 1.41 11.92 10.51
14 0.5 1.48 8.10 11 .31 14 1.0 1.48 12.90 11 .37
234
Predicted velocitr Measured veloclty
0.92
0.87 1.15
0.80 1.13
0.72 1.13
TABLE A.24
EXPERIMENTAL VERIFICATION OF PREDICTED VELOCITY FIELD IN THE CLEAR LIQUID LAYER
Low Aspect Ratio Case
Aspect Ratio, h /b . o . e :
Co : Ao
• R : o
3.42 300
5% v/v 5.32 x 106
1.39
Location of measurement Position Position Predicted Predicted Measured along in clear thickness velocity velocity upper liquid of clear at (x,y) at (x,y) inclined layer liquid surface, normal layer at x (cm) to x, x,oo(mm) mm s-l mm s-l
y (mm)
4 0.5 0.73 6.25 6.30
6 0.5 0.83 7.64 7.63
8 0.5 0.91 8.73 9.50
10 0.5 0.98 9.66 10.60
12 0.5 1.05 10.50 12.38
14 0.5 1.10 11.20 13.56
235
Predicted ve10citl Measured ve 1 oei ty
0.99
1.00
0.92
0.91
0.85
0.83
TABLE A.25
EXPERIMENTAL VERIFICATION OF PREDICTED VELOCITY FIELD IN THE CLEAR LIQUID LAYER
Low Aspect Ratio Case
Aspect Ratio. ho/b : . e : Co : Ao : R . o •
3.78 200
1% v/v 8.52 x 105
2.34
Location of measurement Position Position Predicted Predicted Measured along in clear thickness velocity velocity upper liquid of clear at (x,y) at (x.y) inclined layer liquid surface, normal layer at x (cm) to x. x.oD(mm) mm 5-1 mm 5-1
y (mm)
4 0.5 1.22 2.78 2.95 4 1.0 1.22 4.14 3.36
8 0.5 1.54 3.69 4.53 8 1.0 1.54 5.95 5.24 8 1.5 1.54 6.79 5.16
12 0.5 1. 76 4.33 4.59 12 1.0 1. 76 7.23 6.14 12 1.5 1. 76 8.70 6.49
14 0.5 1.86 4.60 4.79 14 1.0 1.86 7.76 6.30 14 1.5 1.86 9.50 6.69
236
Predicted velocity Measured velocity
0.94 1.23
0.82 1.14 1.32
0.94 1.18 1.34
0.96 1. 23 1.42
TABLE A.26
EXPERIMENTAL VERIFICATION OF PREDICTED VELOCITY FIELD IN THE CLEAR LIQUID LAYER
Low Aspect Ratio Case
Aspect Ratio, ho/b e
3.78 200
2~% v/v 2.67 x 106
1.86
Location of measurement Position Positi on Predicted Predicted Measured along in clear thickness velocity velocity upper liquid of clear at (x,y) at (x,y) inclined layer 1 i qui d surface, normal layer at x (cm) to x, x,oD(mm) mm s-l mm 5-1
y (mm)
4 0.5 0.84 4.18 3.65
8 0.5 l.05 5.74 5.51 8 l.0 l.05 7.90 6.30
12 0.5 1.21 6.83 7.30 12 l.0 l.21 10.08 7.89
14 0.5 l.27 7.28 7.87 14 l.0 1.27 10.98 8.57
237
Predicted velocity Measured ve locl ty
1.15
l.04 1.25
0.99 1.28
0.93 1.28
TABLE A.27
EXPERIMENTAL VERIFICATION OF PREDICTED VELOCITY FIELD IN THE CLEAR LIQUID LAYER
Low Aspect Ratio Case
Aspect Ratio, h/b 3.78 e 200
Co 5% v/v
Ao 6.50 x 106
R . o • 1.53
Location of measurement Position Position Predicted Predicted Measured along in clear thickness velocity velocity upper 1 i qui d of clear at (x,y) at (x,y) inclined layer 1 i qui d surface, normal layer at x (cm) to x, x,oD(mm) mm s-l mm S-l
y (mm)
4 0.5 0.62 5.31 4.57
6 0.5 0.71 6.60 6.28
8 0.5 0.78 7.61 7.30
10 0.5 0.84 8.48 7.28
12 0.5 0.90 9.23 9.20
14 0.5 0.94 9.91 9.85
16 0.5 0.99 10.52 9.63
238
Predicted velocity l1easured velocity
1.16
1.05
1.04
1.16
1.00
1.01
1.09
TABLE A.28
EXPERIMENTAL VERIFICATION OF PREDICTED STEADY-STATE CLEAR LIQUID LAYER THICKNESS
High Aspect Ratio Case
Aspect Rati 0, h/b : 41.31 e : 200
Co : 1% v/v
Ao 5.47 x 106
Ro : 5.93
Pos iti on along Predicted thick- r~easured thick- Predicted thickness upper inclined ness of clear ness of clear Measured thlckness surface, x(cm) liquid layer, liquid layer,
oD (mm) (oD)m' mm
7.5 1. 78 2.31 0.77 10 2.00 2.35 0.85 12.5 2.21 2.41 0.92 15 2.39 2.45 0.97 17.5 2.57 2.51 1.02 20 2.73 2.55 1.07 25 3.05 2.55 1.15 30 3.38 3.00 1.13 35 3.70 3.23 1.15 40 4.05 3.48 1.16 45 4.44 4.00 1.11
239
TABLE A.29
EXPERIMENTAL VERIFICATION OF PREDICTED STEADY-STATE CLEAR LIQUID LAYER THICKNESS
High Aspect Ratio Case
Aspect Ratio, ho/b e
:
:
:
41 .31
300
5% v/v 4.18 x 107
3.88
Positi on a long Predicted thick- Measured thi ck- Predicted thickness upper i ncl i ned ness of clear ness of clear Measured thi ckness surface, x(cm) 1; qui d 1 ayer,
oD (mm) liquid layer,
(oD)m' mm
5 0.71 0.61 1.16
7.5 0.82 0.74 1.11
10 0.91 0.80 1.14
12.5 0.99 0.85 1.16
15 1.06 0.90 1.18
17.5 1.12 0.96 1.16
20 1.18 1.01 1.16
22.5 1.23 1.06 1.16
25 1.28 1.12 1.14
30 1.38 1.17 1.18
35 1.47 1.33 1.10
40 1.54 1.49 1.03
45 1.62 1.57 1.03
240
I
I~
TABLE A. 30
EXPERIMENTAL VERIFICATION OF PREDICTED STEADY-STATE CLEAR LIQUID LAYER THICKNESS
High Aspect Ratio Case
Aspect Ratio, ho/b 64
e 450
Co 1% v/V
Ao 1.31 x la7
Ro 9.18
Position along Predicted thi ck- Measured thick- Predicted thickness upper i nc 1 i ned ness of clear ness of clear Measured thickness surface, x(cm) li qui d layer, liquid layer,
oD (mm) (oD)m' mm
5 2.30 2.79 0.82
7.5 2.78 2.86 0.97
10 3.21 3.04 1.05
12.5 3.66 3.10 1.18
15 4.14 3.18 1.30
241
TABLE A.31
EXPERIMENTAL VERIFICATION OF PREDICTED STEADY-STATE CLEAR LIQUID LAYER THICKNESS
High Aspect Ratio Case
Aspect Ratio, h/b 64 e 450
Co 2~% v/v
Ao 4.13 x 107
Ro 7.31
Position along Predicted thick- Measured thick- Predicted thickness upper i ncl i ned ness of clear ness of clear Measured tfii ckness surface, x(cm) 1 iquid layer, liquid layer,
0D (mm) (oD)m' mm
5 1.44 1.69 0.85 10 1.90 2.18 0.87 15 2.26 2.63 0.86 20 2.57 3.09 0.83 22.5 2.72 3.29 0.83 25 2.86 3.48 0.82 27.5 3.00 3.70 0.81 30 . 3.14 3.87 0.81 32.5 3.28 3.90 0.84 35 3.42 3.94 0.87 40 3.70 4.25 0.87 45 4.00 4.64 0.86
242
TABLE A.32
EXPERIMENTAL VERIFICATION OF PREDICTED STEADY-STATE CLEAR LIQUID LAYER THICKNESS
High Aspect Ratio Case
Aspect Ra ti 0, h/b 64 e 450
Ci 0
.. 5% v/v
110 1 X 108
Ro 6.01
Position along Predicted thick- Measured thi ck- Predi cted thi ckness upper inclined ness of clear ness of clear Measured thickness surface, x( cm) liquid layer, liquid layer,
oD (mm) (oD)m' mm
40 2.35 2.04 1.15 45 2.48 2.10 1.18 50 2.60 2.32 1.12 55 2.73 2.58 1.05 60 2.84 2.80 1.01 62.5 2.90 3.00 0.97 65 2.96 3.12 0.95 67.5 3.02 3.28 0.92 70 3.07 3.40 0.90 72.5 3.13 3.52 0.89 75 3.19 3.61 0.88 80 3.30 3.61 0.91 85 3.42. 3.72 0.92
243
TABLE A.33
EXPERIMENTAL VERIFICATION OF PREDICTED STEADY-STATE CLEAR LIQUID LAYER THICKNESS
High Aspect Ratio Case
Aspect Ratio, h/b : 64 e : 450
c : 10% v/v 0
Ao 2.26 X 108
Ro : 5.33
Position along. Predicted thick- Measured thick- Pred.i cted th i ckness upper inclined ness of clear ness of clear Measured thi ckness surface, x(cm) liquid layer, liquid 1aye·r,
oD (mm) (oD)m' mm
40 1.67 - -50 1.83 1.48 1.23 55 1.90 1.62 1.18 60 1.97 1.80 1.10 65 2.03 2.00 1.01 70 2.10 2.20 0.96 75 2.17 2.40 0.90 80 2.23 2.53 0.88 85 2.29 . 2.83 0.83
244
TABLE A.34
EXPERIMENTAL VERIFICATION OF PREDICTED STEADY-STATE CLEAR LIQUID LAYER·THICKNESS
High Aspect Ratio Case
Aspect Ratio, ho/b e
Co
1.0 R • o
64 450
15% v/v 4.33 x lOB
4.18
Position along Predicted thick- Measured thi ck- Predicted thickness upper inclined ness of clear ness of clear Measured thickness surface, x(cm) liquid layer, liquid layer,
oD (mm) (oD)m' mm
50 1.41 1.09 1.30 55 1.47 1.12 1.32 60 1.52 1.12 1.35 62.5 1.54 1.15 1.33 65 1.56 1.17 1.33 67.5 1.59 1.19 1.33 70 1.61 1. 21 1.33
.
72.5 1.63 1.25 1.33 75 1.65 1.30 1.27 77.5 1.67 1.35 1.23 80 1.69 1.40 1.20 82.5 1.72 1.45 1. 19
245
TABLE A.35
EXPERH1ENTAL VERIFICATION OF PREDICTED STEADY-STATE
CLEAR LIQUID LAYER THICKNESS
High Aspect Ratio Case
Aspect Ratio, ho/b e
:
:
75 300
1% v/v 1.80 x 107
10.76
Pos iti on along Predicted thick- Measured th i ck- Predicted thickness upper incl ined ness of clear ness of clear Measured thi ckness surface, x(cm) liquid layer,
0D (mm) liquid layer,
(oD)m' mm
5 1.82 1.60 1.14 7.5 2.16 2.18 0.99
10 2.46 2.54 0.97 12.5 2.73 3.14 0.87 15.0 2.99 3.77 0.79 17.5 3.24 4.21 0.77 20 3.49 4.53 0.77 22.5 3.75 5.00 0.75 25.0 4.03 5.08 0.79 27.5 4.33 5.44 0.80
246
TABLE A.36 .
EXPERIMENTAL VERIFICATION OF PREDICTED STEADY-STATE CLEAR LIQUID LAYER THICKNESS
High Aspect Ratio Case
Aspect ratio, ho/b 75
e 30° c 2~% v/v
0
Ao 5.67 X 10'
Ro 8.57
Position along Predicted thick- Measured thick- Predicted thickness upper inclined ness of clear ness of clear Measured thlckness surface, x(cm) liquid layer, liquid layer,
oD (mm) (oD)m' mm
45 2.92 3.05 0.96 50 3.08 3.18 0.97 55 3.24 3.43 0.94 60 3.40 3.66 0.93 65 3.56 3.82 0.93 70 3.73 3.92 0.95 75 3.90 4.35 0.90
247
APPENDIX A.2
A.2 OPERATING PERFORMANCE OF THE CONTINUOUS LAMELLA SEPARATOR
A.2.1 Experimental Conditions
Details of suspension
Glass beads:
Size range = 90-125 ~m (spherical)
Particle density = 2460 kg m- 3
Suspension" liqUid:
Reofos 65 (25.5% v/v) & Reomol DBP (74.5% v/v)
Liquid density @ 25°C = 1079.5 kg m- 3
Liquid viscosity @ 250C = (22.2528 x 10-3 ) Ns m-2
Vertical batch settling velocity of suspension:
Concentration of particles in Vertical batch settling suspension (v/v) velocity (vo) cm/s
0.005 0.0287
0.02 0.0243
248
,.- ...
A.2.2 Maximum handling capacity for the pure clear liquid overflow*
TABLE A.37 Maximum Overflow Rate for Countercurrent Flow
Inclination Channel Angle (eO): Length
measured (cm) from the vertical
.
600 49 66 95
112 450 49
66 95
112 300 49
66 95
112 200 49
66 95
112
Feed concentration, Co Number of settling channels Channel spacing, b Channel width, W
Aspect A Ratio of 0
Separator (h/b)
7.21 6.36xl0s 9.71 1.15xl06
13.97 2.39xl06 16.47 3.32xl06
10.19 1.27xl06 13.73 2.31xl06 19.76 4.78xl06 23.29 6 .64xl 06
12.48 1.91xl06 16.81 3.46xi06 24.20 7.17xl06 28.53 9.96xl06 13.54 2. 25xl 06 18.24 4.07xl06 26.26 8.44xl06 30.95 1.17xl07
A ISO referrea to as the ure su ernatan tu' P P sln9 the Nakamura-Kuroda equation 4.24(b)
= 0.5% v/v = 1 = 3.4 cm = 4 cm
Ro Maximum overflow rate Qo (cc/min)
(Qo)expt (Qo) theo t
3.41 340 339.3 4.60 420 440.7 6.61 490 613.5 7.80 580 714.9 4.82 270 271.8 6.50 337.5 354.7 9.35 445.5 495.9
11.03 490 578.6 5.91 205 195.8 7.96 258 254.3
11.45 290 354.3 13.50 350 412.8 6.41 135 140.3 8.64 170 180.4
12.43 190 248.8 14.65 230 288.7
"Efficiency" ratio,
(Qo)expt (Qoltheo
1.00 0.95 0.80 0.81 0.99 0.95 0.90 0.85 1.05 1.01 0.82 0.85 0.96 0.94 0.76 0.80
N U"1 o
Inclination Angle (eO):
measured from the vertical
600
450
300
200
Channel Length (cm)
49 66 95
112 49 66 95
112 49 66 95
112 49 66 95
112
TABLE A.38 Maximum Overflow Rate for Countercurrent Flow Feed concentration, Co Number of settling channels Channel spacing, b Channel width, W
Aspect 110 Ratio of Separator
(h/b)
7.21 3.00x106 9.71 5.45x106
13.97 1. 13x1 07 16.47 1.57x107
10.19 6.01x106 13.73 1.09x107 19.76 2.26x107 23.29 3.14x107 12.48 9.01x106 16.81 1.63x107 24.20 3.39x107 28.53 4.71xl07 13.54 1. 06x107 18.24 1.92x107 26.26 3.99x107 30.95 5.54x10 7
= = = =
Ro
2.89 3.89 5.60 6.60 4.08 5.50 7.92 9.34 5.00 6.74 9.70
11.43 5.43 7.31
10.52 12.41
2% v/v 1 3.4 cm 4 cm
Maximum overflow rate Qo (cc/min)
(Qo)expt (Qo)theo
285 287.3 370 373.1 374 519.5 393 605.3 . 228 230.1 297 300.3 302 419.9 318 489.9 162.5 165.3 209 215.3 210 299.9 227 349.5 115 118.8 145 152.7 160 210.6 170 244.5
"Effi ci ency" ratio,
(Qo)expt (Qo) theo
0.99 0.99 0.72 0.65 0.99 0.99 0.72 0.65 0.98 0.97 0.70 0.65 0.97 0.95 0.76 0.70
N U1 ~
Inclination Angle (eO): measured from the verti ca 1
600
450
300
200
Channel Length (cm)
49 66 95
112 49 66 95
112 49 66 95
112 49 66 95
112
TABLE A.39 Haximum Overflow Rate for Countercurrent Flow Feed concentration, Co Number of settling channels Channel spacing, b Channel width, W
Aspect Ao Ratio of Separator
(h/b)
16.33 6.36xlO5 22.00 1.15xl06
31.67 2.39xl06
37.33 3.32xl06
23.10 1.27xl06 31.11 2.31xl06 44.78 4.78xl06 52.80 6.64xl06
28.29 1.91xl06
38.11 3.46xl06
54.85 7.17xl06
64.66 9.96xl06
30.70 2.25xl06
41.35 4.07xl06
59.51 8.44xl06
70.16 1.17xl07
= = = =
Ro
3.41 4.60 6.61 7.80 4.82 6.50 9.35
11.03 5.91 7.96
11.45 13.50 6.41 8.64
12.43 14.65
0.5% v/v 2 1.5 cm 4 cm
Maximum overflow rate Qo (cc/min)
(Qo)expt (Qo)theo
530 625.8 675 838.7 905 1174.8 945 1377.4 400 506.6 500 672.1 690 954.6 730 1120.3 295 361.4 340 478.5 450 678.2 520 795.3 225 252.9 260 333.0 315 469.6 360 549.7
"Efficiency" ratio,
(Qo)exEt (Qo)theo
0.85 0.81 0.77 0.69 0.79 0.74 0.72 0.65 0.82 0.71 0.66 0.65 0.89 0.78 0.67 0.65
N 01 N
Inclination Angle (eO):
60°
450
300
20°
Channel Length (cm)
49 66 95
112 49 66 95
112 49 66 95
112 49 66 95
112
TABLE A.40 Maximum Overflow Rate for Countercurrent Flow Feed concentration, c = Number of settling chRnnels = Channel spacing, b = Channe 1 wi dth, W =
Aspect A Rati 0 of 0
Separator (h/b)
16.33 3.00xl06 ' 22.00 5 .45xl 06
31.67 1.13x107 37.33 1.57x107
23.10 6.01x106
31.11 1.09x107 44.78 2.26x107 52.80 3.14xl07
28.29 9.01xl06
38.11 1.63xl07 54.85 3.39xl07
Ro
2% v/v 2 1.5 cm 4 cm
2.89 3.89 5.61 6.61 4.08 5.51 7.93 9.35 5.00 6.73 9.69
64.66 4.71x107 11 .42 30.70 1.06xl07 5.43 41.35 1.92xl07 7.33 59.51 3.99xl07 10.55 70.16 5.54xl07 12.43
Maximum overflow rate Qo (cc/mi n)
(Qo)expt (Qo) theo
340 529.9 420 701. 7 580 994.7 662.5 1166.2 270 428.9 370 569.0 450 808.2 530 948.5 200 306 265 405.2 335 574.3 340 673.4 150 214.1 175 281.9 240 397.6 260 465.4
"Effi ci ency" ratio (Qo)ex~t (QoJtheo
0.64 0.60 0.58 0.57 0.63 0.65 0.56 0.56 0.65 0.65 0.58 0.50 0.70 0.62 0.60 0.56
N <n w
Inclination Angle (eO)
600
450
300
200
Channe 1 Length
(cm)
49 66 95
112 49 66 95
112 49 66 95
112 49 66 95
112
TABLE A.41 Maximum Overflow Rate for Cocurrent-Subcritical Flow
Feed concentration, Co Number of settling channels· Channel spacing, b Channel width, W
Aspect Ao Rati 0 of Separator
= 0.5% v/v = 1 = 3.4 cm = 4 cm
Ro Maximum overflow rate Qo (cc/min)
(h/b) (Qo)expt (Qo)theo
7.21 6.36xl0 5 3.41 340 339.3 9.71 1.15xl06 4.60 430 440.7
13.97 2.39xl06 6.61 580 613.5 16.47 3.32xl06 7.80 645 714.9 10.19 1.27xl06 4.82 270 271.8 13.73 2.31xl06 6.50 340 354.7 19.76 4.78xl06 9.35 460 495.9 23.29 6.64xl06 11.03 510 578.6 12.48 1.91xl06 5.91 200 195.8 16.81 3 .46xl 06 7.96 260 254.3 24.20 7.17xl06 . 11.45 305 354.3 28.53 9.96xl06 13.50 365 412.8 13.54 2.25xl06 6.41 145 140.3 18.24 4.07xl06 8.64 180 180.4 26.26 8.44xl06 12.43 190 248.8 30.95 1.17xl07 14.65 235 288.7
"Efficiency" ratio, (Qo)ex~t (Qo)theo
1.00 0.98 0.95 0.90 0.99 0.96 0.93 0.88 1.02 1.02 0.86 0.88 1.03 1.00 0.76 0.81
TABLE A.42 Maximum Overflow Rate for Cocurrent-Subcricital Flow
Feed concentration, c = 2% v/v Number of settling chRnnels = 1 Channel spacing, b = 3.4 cm Channel width, W = 4 cm
Inclination Channel Aspect Ao Ro Maximum overflow rate "Effi ci ency" Angle (eO) Length Ratio of Qo (cc/min ) ratio,
(cm) Separator (Qo)expt. (h/b) (Qo) expt. (Qo)theo. (Qo'theo.
600 49 7.21 3.00xl06 2.89 285 287.3 0.99 66 9.71 5.45x10G 3.89 370 373.1 0.99 95 13.97 1.13x107 5.60 379 519.5 0.73
112 16.47 1.57x107 6.60 400.5 605.3 0.66 450 49 10.19 6.01xl0G 4.08 230 230.1 1.00
66 13.73 1.09xl07 5.50 297 300.3 0.99 95 19.76 2.26xl07 7.92 294 419.9 0.70
112 23.29 3.14xl07 9.34 314 489.9 0.64 300 49 12.48 9.01xl06 5.00 162.5 165.8 0.98
66 16.81 1.63xl07 6.74 209 215.3 0.97 95 24.20 3. 39xl 07 9.70 207 299.9 0.69
112 28.53 4.71xl07 11.43 231 349.5 0.66 200 49 13.54 1.06xl07 5.43 117 118.8 0.98
66 18.24 1.92xl07 7.31 150 152.7 0.98 95 26.26 3.99xl07 10.52 165 210.6 0.78
112 30.95 5.54xl07 12.41 175 244.5 0.72
TABLE A.43 r~aximum Overflow Rate for Cocurrent-Supercritical Flow
Feed concentration, Co = 0.5% v/v Number of settling channels = 1 Channel spacing, b = 3.4 cm Channel width, W = 4 cm
Incl ination Channel Aspect Ao Ro Maximum overflow rate "Efficiency" Angle (eO) Length Ratio of Qo (cc/min) ratio,
(cm) Separator (Qo)expt (h/b) (Qo)expt (Qo)theo (Qol theo
600 49 7.21 6.36xl0s 3.41 340 339.3 1.00 66 9.71 1.15xl06 4.60 440 440.7 1.00 95 13.97 2.39xl06 6.61 590 613.5 0.96
112 16.47 3.32xl06 7.80 645 714.9 0.90 450 49 10.19 1.27xl06 4.82 275 271.8 1.01
66 13.73 2.31xl06 6.50 355 354.7 1.00 95 19.76 4.78xl0 6 9.35 470 495.9 0;95
112 23.29 6.64xl06 11.03 515 578.6 0.89 300 49 12.48 1.91xl06 5.91 210 195.8 1.07
66 16.81 3.46xl06 7.96 270 254.3 1.06 95 24.20 7.17xl06 11 .45 330 354.3 0.93
112 28.53 9.96xl06 13.50 380 412.8 0.92 200 49 13.54 2.25xl06 6.41 145 140.3 1.03
66 18.24 4.07xl06 8.64 190 180.4 1.05 95 26.26 8.44xl0 6 12.43 200 248.8 0.80
112 30.95 1.17xl07 14.65 260 288.7 0.90
N 01 m
Inclination Angle (eO)
600
° 45
30°
200
Channel Length (cm)
49 66 95
112 49 66 95
112 49 66 95
112 49 66 95
112
TABLE A.44 Maximum Overflow Rate for Cocurrent-Supercritical Flow
Feed concentration, Co = 2% v/v Number of set,tling channel's = 1 Channel spacing, b = 3.4 cm Channe 1 ~Ii dth, W = 4 cm
Aspect Ao Ro Maximum overflow rate "Effi ci ency" Ratio of Qo (cc/min) ratio, Separator (Qo)expt
(h/b) (Qo)expt (Qo)theo (QoJtheo
7.21 3.00xl06 2.89 290 287.3 1.01 9.71 5.45xl06 3.89 370 373.1 0.99
13.97 1.13xl07 5.60 405 519.5 0.78 16.47 1.57xl07 6.60 418 605.3 0.69 10.19 6.01xl06 4.08 235 230.1 1.02 13.73 1.09xl07 5.50 305 300.3 1.02 19.76 2.26xl07 7.92 340 419.9 0.81 23.29 3.14xl07 9.34 350 489.9 0.71 12.48 9.01xl06 5.00 165 165.8 1.00 16.81 1.63xl07 6.74 213 215.3 0.99 24.20 3.39xl07 9.70 225 299.9 0.75 28.53 4.71xl07 11.43 248 349.5 0.71 13.54 1.06xl07 5.43 117.5 118.8 0.99 18.24 1.92xl07 7.31 152 152.7 1.00 26.26 3.99xl07 10.52 165 210.6 0.78 30.95 5.54xl07 12.41 185 244.5 0.76
:
N U1 ......
A.2.3 Sludge thickening performance
Inclination Operati ng Angle Time (eO) (mi ns)
70° 0
17 30 45 60 75 90
TABLE A.45 Solids concentration in the underflow (sludge) stream as a
function of the operating time for Countercurrent Flow
Feed concentration, Co Number of settling channels Channel length, L Channel spacing, b Channel width, W
Temperature t~aximum (0C) Overflow Rate
(Qo)expt. cc/min*
25.0 500
25.0 500 24.9 500 25.0 500 24.8 500 25.0 500 25.0 500
= 0.5% v/v = 1 = 66 cm = 3.4 cm = 4 cm
Underflow (sludge) Rate
(Qu)expt. cc/min*
173.8
173.8 173.3 173.8 173.8 173.8 173.8
.
Turbidity level in
the overflow (NTU)
6 (Bac~ground value)
7.0 7.3 7.3 7.0 7.0 7.2
Concentrati on of solids in underfl ow, Cu % v/v
0
0.53 0.74 0.57 0.64 0.58 0.61
* A constant ratio of 3:1 for the overflow rate to the underflow (sludge) rate is maintained throughout the experiment
N U1 (Xl
Inclination Angle (a )
600
TABLE A.46 Solids concentration in the underf10w (sludge) stream as a
function of the operating time for Countercurrent Flow
Feed concentration, Co = 0.5% v/v Number of settling channels = 1 Channel length, L = 66 cm Channel spacing, b = 3.4 vm Channel width, W = 4 cm
Operating Temperature Maximum Underflow Turbidi ty Time (OC) Overflow Rate (sludge) Rate level in
(mins) (Qo)expt. (Qulexpt. the overflow cc/min cc/min (NTU)
0 24.9 420 140.8 b (Background value)
20 24.9 420 140.8 7.2 30 25.0 420 140.8 7.2 45 24.8 420 140.8 7.0 60 25.0 420 140.8 7.0 75 25.0 420 140.8 7.1 90 25.0 420 140.8 7.0
110 25.0 420 140.8 7.0 135 24.9 420. 140.8 7.0 160 24.9 420 140.8 7.1 190 25.0 420 140.8 7.0 205 25.0 420 140.8 7.0
Concentration of solids in underf10w, Cu % v/v
--
1.67 1.67 1. 71 1.77 1.75 1.90 1. 74 1.95 1. 74 1.96
TABLE A.47 Solids concentration in the underflow (sludge) stream as a
function of the operating time for Countercurrent Flow
Feed concentration, Co = 0.5% v/v Number of settling channels = 1 Channel length, L = 66 cm Channel spacing, b = 3.4 cm Channel width, W = 4.cm
Inclination Operati ng Temperature Maximum Underflow Turbidity Concentration Angle Time (OC) Overflow Rate (slud)e) rate level in of sol ids in (eO) (mins) (Qo)expt. (Qu expt. the overflow underflow, c
cc/min cc/min (NTU) % v/v u
450 0 25.0 337.5 113 6 0 (Background value) 30 25.0 337.5 113 7.0 1.65 45 25.0 337.5 113 7.0 1.62 60 24.9 337.5 113 7.2 1.88 75 25.0 337.5 113 7.0 3.27 95 24.9 337.5 113 7.0 1.92
120 24.9 337.5 113 6.9 1.92 135 25.0 337.5 113 7.0 1.91
N en o
Inclination Angle (e )
300
TABLE A.48 Solids concentration in the underf10w (sludge) stream as a
function of the operating time for Countercurrent Flow
Feed concentrati on, co· Number of settling channels Channel length, L Channel spacing, b Channel width, W
= 0.5% v/v = 1 = 66 cm =3.4 cm = 4 cm
Operating Temperature Maximum Underflow Turbidity Time (oC) Overflow Rate (sl udge) rate level in
(mins) (Qo)expt. (Qu)expt. the overflow cc/min cc/min (NTU)
0 24.8 258 84 6 (Background value)
20 25.0 258 84 7.0 30 25.0 258 84 7.2 45 24.9 258 84 7.2 65 25.0 258 84 7.3 90 24.8 258 84 7.0
120 24.9 258 84 7.0 135 25.0 258 84 7.2 150 25.0 258 84 7.0 165 24.9 258 84 7.0
Concentration of solids in underf10w, Cu % v/v
0 1.47 1.66 1.66 2.04 2.52 2.50 2.36 2.41 2.41
TABLE A.49 Solids concentration in the underflow (sludge) stream as a
function of the operating time for Countercurrent Flow Feed concentration. Co = 0.5% v/v Number of settling channels = 1 Channel length. L = 66 cm Channel spacing. b '= 3.4 cm Channel width, W = 4 cm
Inclination Operating Temperature Maximum Underflow Turbidity Concentration Angle Time (oC) Overflow Rate (sludge) rate level in of solids in ( eO) (mins) (Qo)expt. (Qu)expt. the overflow underfl ow, Cu
cc/min cc/min (NTU) % v/v '
200 0 25.0 170 56.3 . 6 0 (Background value) 20 24.9 170
,
56.3 7.2 2.30 35 25.0 170 56.3 7.2 2.25 45 25.0 170 56.3 7.0 2.21 65 25.0 170 56.3 7.0 2.51 75 24.8 170 56.3 7.0 2.16 90 25.0 170 56.3 7.0 3.07
135 24.9 170 56.3 7.0 2.80 150 24.9 170 56.3 7.3 2.99 165 25.0 170 56.3 7.3 2.53 180 25.0 170 56.3 7.2 2.74
N
'" N
Inclination Angle (eO)
600
TABLE A.50 Solids concentration in the underf10w (sludge) stream as a
function of the operating time for Cocurrent-Subcritica1 Flow
Operating Time
(mi ns)
0
35 50 80 90
110 130 145
Feed concentration, Co Number of settling channels Channel length, L Channel spacing, b Channel width, W
Temperature Maximum (OC) Overflow Rate
(Qo)expt. . cc/min
24.9 430
24.9 430 25.0 430 25.0 430 25.0 430 25.0 430 24.9 430 25.0 430
= 0.5% v/v = 1 = 66 cm = 3.4 cm = 4 cm
Underf10w (sludye) rate
(Qu expt .• cc/min
143.3
143.3 143.3 143.3 143.3 143.3 143.3 143.3
Turbi di ty level in
the overflow (NTU)
6 (Background value)
7.0 7.0 7.0 7.0 7.0 7.0 7.0
Con centra ti on of solids in underf1 ow, Cu % v/v
0
1.28 1.49 1.57 1.62 1.56 1.60 1.60
N
'" W
Inclination Angle ( eO)
450
TABLE A.51 Solids concentration in the underflow (sludge) stream as a
function of the operating time for Cocurrent-Subcritical Flow
Operating Time
(mins)
0
80 90
105 120 135 150 165 180
Feed concentration, c Number of settling chRnnels Channel length, L Channel spacing, b Channel width, W
Temperature Maximum (0C) Overflow Rate
(Qo)expt. cc/min
25.0 340
25.0 340 24.8 340
.. 24.9 340 24.8 340 25.0 340 24.9 340 25.0 340 25.0 340
= 0.5% v/v = 1 = 66 cm = 3.4 cm = 4 cm
Underflow (sludge) rate
(Qu)expt. cc/min
112.3
112.3 112.3 112.3 .
112.3 112.3 112.3 112.3 112.3
Turbidity level in
the overflow (NTU)
6 (Background value)
7.0 7.0 7.3 7.3 7.3 7.0 7.1 7.1
Concentrati on of solids in underflow, Cu % v/v
0
1.45 1.73 1.80 2.05 2.02 2.00 2.04 2.02
Inclination Angle ( eO)
300
TABLE A.52 Solids concentration in the underf10w (sludge) stream as a
function of the operating time for Cocurrent-Subcritica1 Flow
Feed concentration, Co Number of settling channels Channel length, L Channel spacing, b Channe 1 wi dth, W
= 0.5% v/v = 1 = 66 cm = 3.4 cm = 4 cm
Operating Temperature Maximum Underf10w Turbidity Time (OC) Ove rfl ow Rate (sludge) rate level in
(mins) (Qo)expt. (Qu)expt. the ove rfl ow cc/min cc/min (NTU)
0 25.0 260 B6.6 6 (Background value)
30 25.0 260 86.6 7.0 45 24.8 260 86.6 7.0 60 24.9 260 86.6 7.2 75 24.9 260 86.6 7.2 90 24.8 260 86.6 7.1
105 24.9 260 86.6 7.2 120 25.0 260 86.6 7.1 130 25.0 260 86.6 7.1
Concentrati on of solids in underf10w, Cu %v/V
0
1. 77 1.77 1.89 1.92 1.89 1.89 1.87 1.87
N en 0"1
Inclination Angle (eO)
20°
,
TABLE A.53 Solids concentration in the underflow (sludge) stream as a
function of the operating time for Cocurrent-Subcritical Flow
Operating Time
(mins)
0
30 45 60 75 90
105 120 135 150 165
Feed concentration, c Number of settling chRnnels Channe 1 1 ength, L Channel spacing, b Channel width, W
Temperature Maximum (0C) Overflow Rate
(Qo)expt. cc/min
25.0 180
25.0 180 24.8 180 24.9 180 24.8 180 24.8 180 24.9 . 180 25.0 180 25.0 180 25.0 180 25.0 180
= 0.5% v/v = 1 = 66 cm = 3 •. 4 cm = 4 cm
Underflow (slud}e) rate
(Qu expt. cc/min
58.3
58.3 58.3 58.3 58.3 58.3 58.3 58.3 58.3 58.3 58.3 .
Turbi di ty level in
the overfl ow (NTU)
6 (Background value)
7.0 7.0 7.0 7.0 7.2 7.0 7.1 7.0 7.0 7.1
Concentration of solids in underfl ow, cu % v/v
0
l. 76 l.77 l.86 2.06 2.24 2.22 2.20 2.20 2.18 2.20
N
'" '"
Inclination Angle ( aO)
600
TABLE A.54 Solids concentration in the underfl0\1 (sludge) stream as a
function of the operating time for Cocurrent-Supercritical Flow
Feed concentration, Co = 0.5% v/v Number of settling channels = 1 Channe 1 1 ength, L = 66 cm Channel spacing, b = 3.4 cm Channel width, W = 4 cm
Operating Temperature Maximum Underflow Turbi di ty Time (0C) Overflow Rate (sludge) ra:':e level in
(mins) (Qo) expt. (Qu)expt. the overflow cc/min cc/min (NTU)
0 24.9 440 146 6 (Background value)
40 25.0 440 146 7.1 60 24.B 440 146 7.1 80 25.0 440 146 7.1
120 24.9 440 146 7.1 140 24.9 440 146 7.1 160 25.0 440 146 7.1 180 24.9 440 146 7.0 195 25.0 440 146 7.0
Concentrati on of solids in underflow, Cu % v/v
0
1.60 1.57 1.57 1. 73 1.90 1.91 1.90 1.90
Inclination Angle (eO)
450
TABLE A.55 Solids concentration in the underflow (sludge) stream as a
fUnction of the operating time for Cocurrent-Supercritical Flow
Feed concentration, Co Number of settling channels Channel length, L Channel spacing, b Channel width, W
= 0.5% v/v = 1 = 66 cm = 3.4 cm = 4 cm
Operating Temperature Maximum Underflow Turbi di ty Time (OC) Overflow Rate (sludge) rate level in
(mins) (Qo)expt. (Qu)expt. the overflow cc/min cc/min (NTU)
0 25.0 355 117.4 6 (Background value)
60 25.0 355 117.4 7.0 80 24.8 355 117.4 7.0
100 24.9 355 117.4 7.0 120 25.0 355 117.4 7.0 140 24.8 355 117.4 7.0 155 24.9 355 117 .4 7.0 175 25.0 355 117.4 7.0 190 24.9 355 117.4 7.0
Concentration of solids in underfl ow, cu %v/V
0
l.84 l.98 2.85 2.68 2.79 2.73 2.79 2.78
N en co
Inclination Angle (eO)
300
TABLE A.56 Solids concentration in the underflow (sludge) stream as a
function of the operating time for Cocurrent-Supercritical Flow
Operating Time
(mins)
0
40 60 80
100 115 130 145 150 180 195
Feed concentration, c Number of settling chRnnels Channel length, L Channel spacing, b Channel width, W
Temperature Maximum (0C) Overflow Rate
(Qo)expt. cc/min
25.0 270
24.9 270 24.8 270 25.0 270 24.8 270 24.9 270 25.0 270 25.0 270 25.0 270 24.9 270 24.9 270
= 0.5% v/v = 1 = 66 cm = 3.4 cm = 4 cm
Underflow (Slud}e) rate
(Qu expt. cc/min
89.8
89.8 89.8 89.8 89.8 89.8 89.8 89.8 89.8 89.8 89.8
Turbidity level in
the overflow (NTU)
6 (Background value)
7.0 7.0 7.0 7.0 7.0 7.0 7.0 7.0 7.0 7.0
Concentrati on of solids in underflow, cu % v/v
0
1.60 1.31 1.68 1.60 1. 71 1.78 1.69 1. 73 1.72 1. 75
N en <0
Inclination Angle ( eO)
200
TABLE A.57 Solids concentration in the underflow (sludge) stream as a
function of the operating time for Cocurrent-Supercritical Flow
Operati ng Time
(mins)
0
50 70 85
100 120 140 160 175
Feed concentration, Co Number of settling channels Channel length, L Channel spacing, b Channel width, W
Temperature Maximum (OC) Overflow Rate
(Qo)expt. cc/min
25.0 190
24.9 190 25.0 190 24.8 190 24.9 190 24.9 190 24.9 190 24.8 190 24.9 190
= 0.5% v/v = 1 = 66 cm = 3.4 cm = 4 cm
Underflow (sludge) rate,
(Q)expt. cc/min
62.5
62.5 62.5 62.5 62.5 62.5 62.5 62.5 62.5
Turbi di ty level in
the ove rfl ow (NTU)
6 (Background value)
7.1 7.1 7.0 7.0 7.1 7.0 7.0 7.0
Concentrati on of solids in underflow, Cu % v/v
0
1. 78 2.02 2.07 2.02 2.22 2.22 2.28 2.25
N ...... o
Inclination Angle (eO)
600
Operating Time
(mins)
0
20
45 65 85
100
TABLE A.58 Solids concentration in the underf10w (sludge) stream as a
function of .the operating time for Countercurrent Flow
Feed concentration, Co = 2% v/v Number of settling channels = 1 Channe 1 1 ength, L = 66 cm Channel spacing, b = 3.4 cm Channel width, W = 4 cm
Temperature Maximum Underfl ow Turbi di ty (0C) Overflow Rate (Sludge) rate, level in
(Qo)expt. (Qu)expt. the overflow cc/min cc/min (NTU)
25.0 370 122 6 (Background value)
24.9 370 122 7.1 24.9 370 122 7.0 24.9 370 122 7.1 25.0 370 122 7.0 25.0 370 122 7.0
Concentrati on of solids in underflow, Cu % v/v
0
6.98 6.95 7.34 7.67 7.72
Inclination Angle (eO)
450
TABLE A.59 Solids concentration in the underf10w (sludge) stream as a
function of the operating time for Countercurrent Flow
Feed concentration, c Number of settling ch~nne1s Channel length, L Channel spacing, b Channel width, W
= 2% v/v = 1 = 66 cm = 3.4 cm = 4 cm
Operating Temperature Maximum Underflow Time (OC) Overflow Rate (sludge) rate
(mins) (Qo)expt. (Qu )expt. cc/min cc/min
Turbidi ty level in
the overflow (NTU)
6 0 25.0 297 99 . (Background value) 20 24.8 297 99 7.0 40 24.9 297 99 7.0 60 25.0 297 99 7.1 80 25.0 297 99 7.0
100 25.0 297 99 7.2
Concentration of solids in underf1 ow, Cu % v/v
0
6.40 7.45 7.40 7.75 7.80
N ...., N
Inclination Angle ( eO)
'.
300
TABLE A.50 Solids concentration in the underflow (sludge) stream as a
function of the operating time for Countercurrent Flow
Feed concentration, Co Number of settling channels Channel length, L Channel spacing, b Channel width, W
= 2% v/v = 1 = 66 cm = 3.4 cm = 4 cm
Operating Temperature Maximum Underflow (0C) Time Overflow Rate (sludge) rate
(mins) (Qo)expt. (Qu) expt. . cc/min cc/min
.
Turbi dity level in
the overflow (NTU)
6.1 0 24.9 209 70 (Background value) 20 25.0 209 70 7.2 30 25.0 209 70 7.0
50 24.8 209 70 7.1 70 24.9 209 70 7.0 90 25.0 209 70 7.0
100 25.0 209 70 7.0
Concentrati on of solids in underfl ow, Cu %v/V
0
7.5 7.4 7.6 7.8 8.0
7.9
N ...., W
Inclination Angle (eO)
200
TABLE A.61 Solids concentration in the underflow (sludge) stream as a
function of the operating time for Countercurrent Flow
Feed concentration, c Number of settling chRnnels Channe 1 length, L Channel spacing, b Channel width, W
= 2% v/v = 1 = 66 cm = 3.4 cm = 4 cm
Operating Temperature Maximum Underflow Time (OC) Ove rfl ow Ra te (sludge) rate
(mins) (Qo) expt. (Qu)expt. cc/min cc/min
Turbidi ty level in
the overflow (NTU)
6 0 25.0 145 48 (Background value) 20 25.0 , 145 48 7.0 40 24.9 145 48 7.0 55 24.9 145 48 7.0 70 25.0 145 48 7.0 85 24.8 145 48 7.0
100 25.0 145 48 7.1 .
Concentration of solids in underflow, Cu % v/v
0
7.75 7.99 8.20 8.27 8.00 8.35
Inclination Angle (eO)
600
TABLE A.62 Solids concentration in the underf10w (sludge) stream as a
function of the operating time for Cocurrent-Subcritica1 Flow
Operating Time
(mins)
0
20 40 60 80
100
Feed concentration, Co Number of settling channels Channel length, L Channel spacing, b Channel width, W
Temperature Maximum (0C) Overflow Rate
(Qo) expt. cc/min
25.0 370
24.8 370 25.0 370 24.9 370 24.8 370 24.9 370
= 2% v/v = 1 = 66 cm = 3.4 cm = 4 cm
Underflow (s 1 udge) rate
(Qu)expt. cc/min
124.5
124.5 124.5 124.5 124.5 124.5
Turbidity level in
the overflow (NTU)
6 (Background value)
7.0 7.0 7.0 7.1 7.0
Concentrati on of solids in underf1 ow, Cu % v/v
0
7.03 7.19 6.59 7.26 7.13
TABLE A.63 Solids concentration in the underflow (sludge) stream as a
function of the operating time for Cocurrent-Subcritical Flow
Feed concentration, Co = 2% v/v Number of settling channels = 1 Channel length, L = 66 cm Channel spacing, b = 3.4 cm Channel width, W = 4 cm
Incl ination Operati ng Temperature Maximum Underflow Turbidity Concentration Angle Time (0C) Overflow Rate (sl udge) rate, level in of solids in (eO) (mins) (Qo)expt. (Qu)expt. the overflow underflow, Cu
cc/min cc/min (NTU) % v/v
450 0 25.0 297 99.5 6 0 (Background value) 20 25.0 297 99.5 7.0 7.57 40 25.0 297 99.5 7.0 7.30 -60 24.8 297 99.5 7.0 7.50 80 25.0 297 99.5 7.0 7.21
100 24.9 297 99.5 ·7.0 7.18
TABLE A.64 Solids concentration in the underflow (sludge) stream as a
fUnction of the operating time for Cocurrent-Subcritical Flow
Feed concentration, Co = 2% v/v Number of settling channels= 1 Channel 1 ength, L = 66 cm Channel spacing, b = 3.4 cm Channel width, W = 4 cm
Inclination Operating Temperature Maximum Underflow Turbi di ty Concentrat ion Angle Time (OC) Overflow Rate (sludge) rate, level in of sol ids in (eO) (mins) (Qo)expt (Qu)expt the overflow underflow, Cu
cc/min cc/min (NTU) % v/v
300 0 25.0 209 70 6 0 (Background value) 20 24.9 209 70 7.0 B.02 40 25.0 209 70 7.0 7.85 60 24.9 209 70 7.1 7.76 80 24.9 209 70 7.1 7.60
100 24.8 209 70 7.0 7.70
Inclination Angle (eo)
200
TABLE A.65 Solids concentration in the underf10w (sludge) stream as a
function of the operating time for Cocurrent-Subcritica1 Flow
Operating Time (mins)
0
20 40 60 80
100
Feed concentration, c Number of settling chRnnels Channel length, L Channel spacing, b Channel width, W
Temperature Maximum (OC) Ove rfl ow Ra te
(Qo) expt. cc/min
25.0 150
25.0 150 25.0 150 24.9 150 24.9 150 25.0 150
= 2% v/v = 1 = 66 cm = 3.4 cm = 4 cm
Underflow (sludge) rate,
(Qu) expt. cc/min
50
50 50 50 50 50
Turbidity level in
the overflow (NTU)
6 (Background value)
7.0 7.0 7.2 7.0 7.0
Concentration of solids in underflow, Cu % v/v
0
8.01 7.88 7.79 7.91 7.88
N ...., co
Inclination Angle (e )
600
TABLE A.66 Solids concentration in the underf10w (sludge) stream as a
function of the operating time for Cocurrent-Supercritica1 Flow
Operating Time (mins)
0
20 40 60 90
100
Feed concentration, Co Number of settling channels Channe 1 1 ength, L Channel spacing, b Channel width, W
Temperature Maximum (OC) Overflow Rate
(Qo)expt. cc/min
24.9 370
24.8 370 24.9 370 25.0 370 24.9 370 25.0 370
= 2% v/v = 1 = 66 cm = 3.4 cm = 4 cm
Underf10w (sludge) rate,
(Qu)expt. cc/min
125.3
125.3 125.3 125.3 125.3 125.3
Turbidity level in
the overflow (NTU)
6.1 (Background value)
7.1 7.2 7.2 7.1 7.2
Concentration of sol ids in underf10w, Cu % v/v
0
6.23 7.55 7.46 7.61 7.60
N ...... '"
Inclination Angle ( eO)
45°
TABLE A.67 Solids concentration in the underf10w (sludge) stream as a
function of the operating time for Cocurrent-Supercritica1 Flow
Opera ting Time (mins)
0
20 40 60 80
100
Feed concentration, Co Number of settling channels Channel length, L Channel spacing, b Channel width, W
Temperature Maximum (0C) Overflow Rate
(Qo)expt. cc/min
25.0 305
24.9 305 24.8 305 24.9 305 24.9 305 25.0 305
= 2% v/v = 1 = 66 cm = 3.4 cm = 4 cm
Underf10w (sludge) rate.
(Qu)expt. cc/min
102
102 102 102 102 102
Turbidity level in
the overflow (NTU)
6 (Background value)
7.0 7.0 7.0 7.0 7.0
Concentration of solids in underflow, Cu % v/v
0
7.52 7.68 7.67 7.69 7.75
N 00 o
Inc1 ination Angle ( eO)
300
TABLE A.68 Solids concentration in the underf10w (sludge) stream as a
function of the operating time for Cocurrent-Supercritica1 Flow
Operating Time (mins)
0
20 40 60 80
100
Feed concentration, Co Number of settling channels Channel length, L Channel spacing, b Channel width, W
Temperature Maximum (OC) Overflow rate
(Qo)expt. cc/min
25.0 213
24.9 213 24.8 213 24.8 213 25.0 213 24.9 213
= 2% v/v = 1 = 66 cm = 3.4 cm = 4 cm
Underflow (sludge) rate,
(Qu)expt. cc/min
71
71
71
71 71
71
Turbidity level in
the overflow (NTU)
6 (Background value)
7.0 7.0 7.0 7.0 7.0
Concentrati on of solids in underflow, Cu % v/v
0
7.99 7.62 7.59 7.82 7.69
N 00 ~
rncl ination Angle (eO)
200 -
TABLE A.69 Solids concentration in the underflow (sludge) stream as a
function of the operating time for Cocurrent-Supercritical Flow
Feed concentration, c = 2% v/v Number of settling chRnnels = 1 Channel length, L = 66 cm Channel spacing, b = 3.4 cm Channel width, W = 4 cm
Operating Temperature Maximum Underflow Turbidity Time. (OC) Ove rfl ow ra te , (sludge) rate, 1 eve 1 in (mins) (Qo)expt. (Qu) expt. the overflow
cc/min cc/min (NTU)
0 25.0 152 49.4 6 (Background value) .
20 24.8 152 49.4 7.0 40 24.9 152 49.4 7.0 60 24.8 152 49.4 7.0 30 25.0 152 49.4 7.0
100 24.9 152 49.4 7.0
Concentration of solids in underflow, Cu .
% v/v
0
8.07 7.92 7.76 8.08 7.93
SymboL
b
B
c
D
->e
F
g
h
L
p
p
NOMENCLATURE
Description
channel spacing (plate spacing)
dimensionless channel spacing
volume fraction of particles in suspension
concentration (volume fraction of particles) in feed t6 separator
concentration of particles in underflow from separator
hydraulic diameter of settling channel
unit vector in the direction of gravity
empirical coefficient in Graham and Lama's equation
gravitational constant
solids flux in a continuous vertical settler
solids flux in a continuous inclined settler
limiting solids flux in a continuous settler
additional solids flux contributed by the inclined surfaces
vertical height of suspension measured from the base of the upper inclined surface at time t (or characteristic length of the macroscale motion)
length of lamella plate
dimensionless absolute pressure
dimensionless kinetic pressure
282
Dimensions
L
L
L
L
Symbo~
n
N
s
T
u
u
v
v
w
x
Description
nUr.lber of settl ing ch an ne 1 s
number of fringes in rms laser beam radius
sedimentation Grashof number
sedimentation Reynolds number
volumetric flow rate through the separator
volumetric feed rate to separator
volumetric overflow rate from separator
volumetric underflow rate from separator
fringe spacing (laser beams)
time
particle residence time in settling channel
dimensionless time
longitudinal component of velocity in clear liquid layer
dimensionless longitudinal component of velocity in clear liquid layer (i.e. along the direction of the upper inclined surface)
vertical settling velocity of particles in suspension
dimensionless velocity component in clear liquid layer normal to the upper inclined surface
width of lamella plate
distance along the upper inclined surface, measured from its base
283
Dimensions
L
T
T
LT-l
L
L
Symbo~
x
y
y
a
T)
e
A
]l
1T
P
Pp
psusp •
Description
dimensionless distance along the upper inclined surface measured from its base
distance measured from and normal to the upper inclined surface
dimensionless value of y
angle of inclination (from the horizontal)
clear liquid layer thickness (measured from and normal to the upper inclined surface)
dimensionless clear liquid layer thickness
turbulence intensity of measured velocity
angle of inclination (from the vertical)
wavelength of He-Cd laser beam
ratio of sedimentation Grashof number to the sedimentation Reynolds number
viscosity of pure fluid
refractive index of the suspension liquid medium
effective viscosity of suspension di vi ded by ]l
pi constant
density of pure fluid
density of particles
effective density of suspension
284
Dimensions
L
degrees
L
degrees
L
Symbo~ Desaription
p(~) effective density of suspension divided by that of the pure fluid
Subscript •.
110"
Superscript
density difference between the suspension and pure fluid
local particle concentration divided by that of the initial concentration of suspension, Co
denotes initial value
denotes stretched variables
285
Dimensions
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