Table Of ContentFLUID
MIXING II
A symposium organised by the
Yorkshire Branch and the Fluid Mixing
Processes Subject Group of the
Institution of Chemical Engineers
and held at Bradford
University, 3-5 April 1984
Organising Committee:
Prof. M.F. Edwards
Dr. N. Harnby
Dr. J.C. Middleton
THE INSTITUTION OF CHEMICAL ENGINEERS
SYMPOSIUM SERIES No. 89
(i)
PUBLISHED BY THE INSTITUTION OF CHEMICAL ENGINEERS
Copyright ö 1984 The Institution of Chemical Engineers
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British Library Cataloguing in Publication Data
Fluid mixing II. - (Institution of Chemical Engineers
symposium series: 89)
1 Mixinq 2. Fluid dynamics
' institution of Chemical Engineers, Yorkshire Branch
ii. Institution of Chemical Engineers, Fluid Mixing
Processes Subject Group
III. Series
660.2'84292 TP156.M5
Pergamon Press ISBN 0-08-031416-3
Library & Congress No. 84-14849
(ii)
PREFACE
Fluid Mixing II continues the series of
conferences which began at Bradford in March
1981. It is hoped to hold a third in the series in
1987. The conferences are intended to cover all
aspects of mixing including the assessment of
mixture quality, experimental and theoretical
studies of mixing, chemical reaction and mass
transfer, heat transfer, novel experimental
techniques, scale-up and optimisation. The
authors represented include most of the
leading names in the field in the UK and
Continental Europe.
Symposium Series No. 89
THE DRAWDOWN OF FLOATING SOLIDS INTO MECHANICALLY AGITATED VESSELS
M. F. Edwards and D. I. Ellis
Schools of Chemical Engineering, University of Bradford.
SYNOPSIS
Data are reported of the critical impeller speed required to draw float
ing solids down into the bulk of the liquid in a cylindrical vessel of
diameter 1.22 m. A variety of impeller types and baffle configurations
was studied. In each case water was the test liquid and various concen
trations of polyethylene chips were used.
Measurements were taken of the power input at the minimum drawdown speed
and these are used to assess the optimum impeller/baffle arrangement.
INTRODUCTION
The use of agitated vessels to contact solids and liquids is encountered
in a number of industrially important processes. The basic objective
may be to provide intimate contact between the two phases to facilitate
mass transfer or chemical reaction, or simply to produce a general dis
persion of the solid particles in the liquid prior to hydraulic transport
through pipelines and processing equipment. In either case a major de
sign consideration is the appropriate impeller speed to achieve good con
tacting conditions using a minimum input of power.
In the case of solids which are denser than the liquid, much work has
been done to establish relationships between the minimum speed required
for complete suspension of the solids, Njs, and the potentially large
number of system parameters involved. An early, comprehensive and fre
quently quoted study is that of Zwietering (1), who proposed the follow
ing empirical correlation:-
ϊθ.45
0.1
N. = s v d — D-°·85 X0·13 (1)
P
where s is a constant for a given type of impeller and system geometry.
Here Njs is the impeller speed which is just sufficient to prevent the
particles from remaining "stationary" on the base of the tank and various
criteria have been put forward to define this suspension state in which
all of the surface area of the particles becomes effective for processing.
More recent works (e.g. (2,3,4)) have considered a wider range of geomet
rical configurations than those used by Zwietering (1). In particular
impeller types, the height of the impeller above the base, the size and
location of draught tubes have all been studied in an attempt to achieve
adequate suspension conditions with a minimum of power input.
In certain effluent treatment, polymerisation and fermentation processes,
it is often necessary to contact solids which are less dense than the
1
Symposium Series No. 89
liquid. This problem of the drawdown of floating solids has received very
little attention, the only major investigation being that reported by
Joosten et al (5). These authors found that for vessel sizes from 0.27
to 1.8 m the baffle arrangement was critical. It was observed that the
optimal flow pattern for drawdown was achieved with a single baffle (one
fifth of the tank diameter in width) leading to an eccentric vortex.
Using this baffle configuration, a four bladed angled paddle of diameter
0.6 times the tank diameter required the least power input compared to
other 2, 4 and 6 bladed angled paddles and 3 bladed marine propellers.
The minimum speed for drawdown was correlated by:-
= 3 b xl {2>
-i~ - ° ITJ [T]
for the preferred stirrer/baffie arrangement (one baffle 0.2 T/four bladed
inclined paddle).
Ohiaeri (6) carried out some experiments with floating solids and conclu
ded that propellers were more efficient than pitched paddles and that the
best geometry is achieved with the impellers located near tne liquid sur
face and pumping upwards. These comments were applicable to tanks of
diameter 0.3 to 0.91 m fitted with four baffles.
The present study reports information on a series of tests in which the
minimum drawdown speed and the associated power requirement have been
measured in a 1.22 m diameter flat bottomed vessel with a variety of impel
ler and baffle configurations.
EXPERIMENTAL WORK
Equipment
Measurements of the minimum drawdown speed and the associated power requi
rement were carried out in a 1.22 m diameter flat bottomed, cylindrical
vessel. Up to four vertical strip baffles could be inserted at various
positions around the periphery of the vessel, with essentially no clear
ance between the outer edge of the baffle and the vesse lwall. Each baf
fle had a width equal to one-tenth of the tank diameter and could be arran
ged to rest on the bottom of the vessel or be raised to give a clearance
of 0.305 m between the lower edge of the baffle and the base of the vessel.
When the baffles were in the lowered position their wetted length was
equal to the depth of liquid in the vessel, which was maintained through
out at 1.15 m. The range of baffle configurations investigated is detail
ed in Table 1.
Agitation was provided by three impellers; a downward pumping, 3-bladed
marine propeller, a six-bladed disc turbine and a simple flat paddle. The
principle dimensions are shown in Figure 1. The impellers were mounted
on a 4.5 cm diameter mild steel shaft which was located on the axis of the
vessel and was driven by a 2.54 kW motor through a variable speed drive
and a 3.98:1 reduction gear, giving a range of rotational speeds of 1.06
to 12 rev/s. The whole drive unit was vertically mounted on a thrust bear
ing comprising a fixed base plate and a well-greased ball race. A parall
elogram mechanical linkage transmitted the torque produced on the motor
assembly to a load cell. Assuming that the friction loss in the linkage
2
Symposium Series No. 89
TABLE 1
Baffle Configurations Used
The configurations used are identified by the coding m/n. m is the total
number of baffles, n the number in the raised position.
Number of Arrangement around
Codes
baffles vesselo perip hery
1 o I/O, 1/1
2 o 2/0, 2/1, 2/2
2A/0, 2A/1, 2A/2
o
2B/0, 2B/1, 2C/2
o
3 3/0, 3/1,
3/2, 3/3
4 G 4/0, 4/1, 4/2a,
4/2b, 4/3, 4/4
(4/2a - two opposed
baffles rai
sed
4/2b - two adjacent
baffles rai
sed)
and the ball race is negligible, the load cell reading gives a direct mea
sure of the torque on the shaft and hence the power consumption of the
impeller. The speed of rotation of the impeller was taken from the motor
shaft coupling using a mechanical tachometer.
Throughout the experimental work the liquid used was water and the parti
cles were high density polyethylene chips having a size range of 1.4 -
3.35 mm and a density of 925 kg/m3. For all three impellers used, measure
ments of the minimum suspension speed, N, and the corresponding power
s
requirement, p i were made for each of the 22 different baffles config
m n/
urations shown in Table 1 and for solid concentrations of 0.75, 1.5, 2.25,
3.0 and 3.75% w/w. All these experiments were performed with the impel
lers located to give a clearance between each impeller and the bottom of
3
Symposium Series No. 89
the vessel of V rdof the liquid depth. In addition, N and pj_n were
3 s m
measured for the propeller and the turbine using a concentration of 3.75%
w/w but with an impeller clearance of 2/3rd of the liquid depth. The sim
ple paddle could not readily be raised into this position.
Procedure
In each series of runs, the speed of the impeller was progressively
increased from its minimum value until the minimum speed for complete
drawdown was adjudged to have been reached. The determination of the
minimum suspension speed was based on a criterion similar to that used by
Zwietering (1). Thus, when a stagnant zone, even one consisting of only
a few floating polyethylene chips, stayed on the surface for less than
3-5 seconds, the drawdown was considered to be just complete. On this
basis, it was possible for the same observer to determine the minimum
impeller speed for complete suspension with a reproducibility of 2 - 7%.
RESULTS
Effect of Concentration
For each impeller the general effect of concentration on minimum suspen
sion speed was essentially insignificant. This may be illustrated, for
example, by the data obtained for the turbine, as seen in Figure 2 for a
range of different baffle configurations. Very similar results were obta
ined for the paddle and for the propeller, although in the latter case a
considerable scatter of the experimental values of N was observed when a
s
single baffle was used (configurations 1/0 and 1/1). This resulted from
the difficulty experienced in applying the basic criterion for complete
suspension under these conditions, particularly at the higher concentra
tion levels. Thus with a single baffle the solids were largely suspended
by the gross vortex produced. However, to reach the centre of the vortex
the majority of the floating particles had to travel around the tan kperi
phery until the rising swell produced immediately behind the baffle direc
ted them into the vortex.
In attempting to correlate the observed power consumption at minimu msus
pension speed, Pmin* it was found that the data were widely scattered when
represented as a function of concentration for all baffle configurations.
This is illustrated by the results obtained for the turbine, as shown in
Figure 3. Whilst large variations in Pmin a*"e apparent, no consistent
pattern may be discerned. These large variations are, however, very much
reduced when the power consumption is represented in terms of the power
number, Po = Pmin/P Ns D · Thus reference to Figure 4, which includes
data for all three impellers and baffle configurations 1/0, 2/0, 3/0 and
4/0, shows that Po is essentially independent of concentration. Bearing
in mind the relative low concentration levels involved, this result is
not surprising. It does, however, suggest that the small variations in
N observed at different concentration levels (see Figure 2) are suffi
s
cient, when incorporated into Po, to compensate for the relatively large
variations observed for Pmin (see Figure 3).
Effect of Impeller Type
Of the parameters investigated, the impeller type used had a major effect
on both N and Pmin· Tne influence on N is shown very clearly in Table 2
s s
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Symposium Series No. 89
which includes the average values of N for all baffle configurations and
s
particle concentrations at the lower impeller clearance.
TABLE 2
Mean Values of N and Associated Standard Deviation
s
(impeller clearance, c = V3 H)
Ns r.p.m.
Turbine Propeller Paddle
Unbaffled (mean
129* (-) 180 (+_ 5) 93 (+_ 11)
for all concns.)
Baffled (mean
for all concns.
126 ( + 6) 223 (+12) 120 (+ 9 )
and baffle con
figurations)
*
based on single value for X = 3.75%
Thus N was observed to be very much higher for the propeller than for
s
either the turbine or the simple paddle. Furthermore, the mean value of
N for the turbine was significantly higher than for the paddle.
s
Typical values of Pmin f°r all three impellers tested are shown in Figure
5, which incorporates the full range of baffle configurations examined at
an arbitrarily chosen particle concentration level of 2.25%. The results
clearly show that the power requirement for the propeller is substantially
less than for either the paddle or the turbine and that this trend is more
evident as the number of baffles is increased. It is also evident that
drawdown is generally achieved with lower pov/er requirements as the number
of baffles is reduced. This trend is more noticeable for the paddle and
the turbine than for the propeller.
Effect of Baffle Configuration
As evidenced by the data shown in Figure 2 which includes results for
different numbers of baffles and for the baffles in the raised and lowered
positions (configurations 1/0, 1/1, 2/0, 2/2, 3/0, 3/3 and 4/0, 4/4), the
baffle configuration has little or no effect on the minimum suspension
speed. Similar results were found for the propeller and the simple paddle.
In the absence of any baffles, the propeller gave a significantly lower
value of N than for any of the baffled arrangements, as shown in Table 2.
s
The latter also shows that there was a similar, although rather less sig
nificant effect for the paddle. In the case of the turbine, complet esus
pension could not be obtained in the absence of baffles except at a parti
cle concentration of 3.75% with the lower impeller clearance.
5
Symposium Series No. 89
For each impeller the power requirement tended to increase as the number
of baffles was increased and was generally greater when one or more of the
baffles were in the raised position. As noted previously, however, con
siderable scatter was observed in the basic data, for Pmirw see Figure 5.
Effect of Impeller Clearance
Measurements of Ns and Pmin were obtained for the turbine and propeller,
but not the paddle, with the impeller raised to give a clearance of 2/3 Qf
the liquid depth above the base of the vessel. A wide range of baffle
configurations was examined using a particle concentration of 3.75'*. w/w.
The effect of impeller clearance at this concenti iticr: I s shv ile 3
for a selection of baffle configuration-..
TABLE 3
Influence of Impeller Clearance (for X = .>.7s3
N (c = ^3 H) P . (c = L/3 H)
Baffle min
Impeller
Configuration N (c = 2/3 H) P~~ (c = 2/3 H)
s mm
Turbine 1/0 1.18 1.52
1/1 1.21 1.25
2/0 1.00 0.94
2/2 1.12 1.39
3/0 1.17 1.47
3/3 1.21 1.74
4/0 1.44 2.70
4/4 1.32 2.31
Propeller 1/0 1.21 3.90
1/1 1.35 3.40
3/3 1.03 1.15
4/0 1.10 1.70
4/4 1.05 1.19
These results indicate that whilst the effect on Ns of changing the clear
ance is relatively small there is a substantial effect on the power requi
rement. Thus, reducing the clearance from 2/3 to 1/3 of the liquid depth
increased the values of Ns and Pmin by average factors of 1.2 and 1.7 for
the turbine and 1.15 and 2.3 for the propeller.
From Table 3 it can be seen that increasing the clearance above the base
gives the most significant power saving for the turbine when four baffles
are used. For the propeller the greatest power reduction is observed for
single baffle systems.
Joosten et al (5) also observed a small effect of clearance upon Ns.
Further, they also found a general decrease in power input with increa
sing clearance (except for their 6 bladed inclined paddle).
6
Symposium Series No. 89
CONCLUSIONS
a) Measurements have been made in a 1.22 m vessel of the impeller speed
and power requirement for the drawdown of 1.4 - 3.35 mm polyethylene
chips into water. For such large particles the inter-particle forces
are negligible and there is no problem in wetting clusters, of parti
cles after drawdown.
b) The effect of particle concentration upon both the minimum drawdown
speed and the associated power input is insignificant over the range
of concentrations used (0.73 - 3.75% w/w\.
c) The lowest power requirements were found using propellers and in gene
ral reducing the number of baffles also reduced the power input. In
the case of zero baffles, the power requirements were so low that they
could not be measured with great accuracy. This confirms the often
quoted teclinique of "pouring solids down the vortex into a vessel".
However, it should be noted that since the power input in such vortex-
ing situations is very low, the turbulent stresses in the fluid may
not be sufficient to break up clumps of particles when fine powders
are added.
d) The position of the impeller above the base of the tank can signifi
cantly influence the power required for drawdown.
SYMBOLS
c clearance of impeller above base
d particle size
P
D impeller diameter
g gravitational acceleration
H liquid depth
N. minimum suspension speed
N minimum drawdown speed
p . power at minimum drawdown speed
Po power number
s constant in Equation (1)
T vessel diameter
X solids concentration
p liquid density
Δρ density difference between solid and liquid
v kinematic viscosity
7
