EFFECT OF COHESIVE INTERPARTICLE FORCES ON
MINIMUM FLUIDIZATION VELOCITY AT HIGH
TEMPERATURES
Ammendola Paola and Chirone Riccardo
Istituto di Ricerche sulla Combustione IRC-CNR
P.le V. Tecchio, 80 – 80125 Napoli – Italy
Tel. [39] 081 7682242; fax [39] 081 5936936 – E-mail: chirone@irc.na.cnr.it
ABSTRACT
Pressure drops and bed expansion curves have been obtained to establish the
influence of temperature on minimum fluidization velocity, terminal velocity,
Richardson and Zaki exponent and size of fluidized particles for three different
materials belonging to Groups A, B and C of Geldart classification. Experiments
have been carried out by means of a laboratory scale fluidized bed operated with
and without the application of acoustic fields having different intensities and
frequencies, at temperatures varying from ambient temperature up to 600°C. The
experimental results have been interpreted on the basis of a simple model predicting
the effectiveness of sound assisted fluidization in reducing interparticle forces.
INTRODUCTION
The interest in handling relatively fine particles in various industrial processes
carried out at thermal levels above ambient conditions raises the question of the
caution in scaling up cold models not only in the case of cohesive particles, which
belong to Geldart’s C powders but also of powders classified as A (1) or B (2). Very
few indications are reported in literature on the effect of temperature on fluidization
quality. Yates (3) found that the correlations obtained at ambient temperature can
still be used at high temperatures when variations of density and viscosity of gas
and a correct value of the minimum fluidization voidage are used. However it is not
clear how temperature influences the minimum fluidization bed voidage. Pattipati
and Wen (4), found for a Group B material that it is not dependent on temperature.
On the other hand, Botterill et al. (5), found that it depends on both temperature and
particle size. Raso et al. (6) and Formisani et al. (7) found a moderate increase in
minimum fluidization voidage with temperature.
The influence of interparticle forces on fluidization behaviour has been
suggested by various Authors (8-11, 2). Formisani et al. (8) indicated the increase in
interparticle forces as the cause for temperature-dependence of particulate phase
voidage and minimum fluidization velocity. Lettieri et al. (9-10) found that, depending
on the material, fluidization behaviour can be dominated by interparticle forces. In
this case, they found that the exponent of Richardson-Zaki (12) and the terminal
velocity were much higher than those predicted by literature correlations (12,13).
Also Geldart and Wong (11) found high values (4–60) of Richardson-Zaki exponent
associated with high degrees of cohesiveness of materials. Lin et al (2) found a nonmonotonous trend of minimum fluidization velocity for a Group B material. Even if no
direct evidence on the effect of interparticle forces on fluidization behaviour has
been proved, there is a general consideration that they may play a role also in the
case of Groups A and B materials. Very few indications are reported in the literature
on the effect of temperature on solid-to-solid forces. With reference to van der
Waals forces (14), the interparticles forces that prevail during high temperature
fluidization, Osborne and Lee (15) and Visser and Maassluis (16) found that for
different materials the Hamaker constant is rather insensitive to temperature.
Differently, Krupp (17), Veli-Matti Kerminen (18) and Petrazzuolo (19) found a strong
influence of temperature.
A systematic approach to characterize the effect of temperature on the
fluidization of three different powders of Groups A, B and C of Geldart classification,
has been carried out in this work. Pressure drops and bed expansion curves have
been obtained to establish the influence of temperature on minimum fluidization
velocity, terminal velocity, Richardson and Zaki exponent and size of fluidized
particles. The relevance of interparticle forces on fluidization has been highlighted
by carrying out experiments under sound assisted conditions. A simple model has
been developed to account for the role played by van der Waals forces on the size
of fluidized particles for a multi-sizes Group A powder.
EXPERIMENTAL APPARATUS AND TECHNIQUE
The experimental apparatus used is
shown in Fig.1. Tests were carried out
with or without application of acoustic field
with intensity and frequency varying
between 130 and 150dB and 50 and
300Hz respectively. Tests were carried
out at a temperature ranging from ambient
temperature up to 600°C and using
nitrogen from cylinders as fluidizing gas.
Three different materials were used:
ashes collected at the exit of a fluidized
bed combustor and two silica sand
powders. Their properties are reported in
Table I.
Experiments aimed at characterizing the
minimum fluidization velocity. Pressure
drops and bed expansion curves as a
function of gas velocity were measured in Figure 1. Experimental Apparatus: 1) preexperiments carried out at different heater; 2) electric heaters; 3) 40mm ID
fluidization column; 4) sound guide; 5)
temperatures. Beds made of 180g were microphone; 6) loudspeaker; 7) monometer; 8)
used for Group A and B materials. thermocouple.
Experimental data were worked out to
calculate bed voidage at minimum fluidization conditions and, according to Ergun
correlation (20), average size of fluidized particles.
Experiments aimed at characterizing the terminal velocity and the Richardson and
Zaki exponent. Bed expansions curves as a function of gas velocity have been
measured in experiments carried out at different temperatures under homogeneous
expansion regime of a bed made of 180g of Group A material. Experimental data
were worked out to obtain terminal velocity and Richardson and Zaki exponent.
According to Stokes correlation, terminal velocities were further worked out to
calculate the average size of fluidized particles.
Table I. Properties of tested materials
Experiments aimed at highlighting
the relevance of interparticle forces
Ashes Silica sand Silica sand
on fluidization behaviour. Pressure
< 80
6-146
300-400
Particle size, (µm)
drops and bed expansion curves as
a function of gas velocity were
8
60
340
Sauter diameter, (µm)
measured in experiments carried
Apparent density,
2000
2600
2600
out at different temperatures and
3
(kg/m )
using acoustic fields of different
Sphericity factor
0.5
0.73
0.73
intensities
(130-150dB)
and
Gerdart Classification
C
A
B
frequencies (50-300Hz). Beds made
of 180g of Groups A and B powders
and 80g of Group C powder were
used. Experimental data were worked out to calculate minimum fluidization
velocities and bed voidages for all materials and, only for Groups A and C, terminal
velocities and Richardson and Zaki exponents. The average sizes of fluidized
particles were evaluated according to Ergun and Stokes correlations.
THEORY
forces, N
Adi/Ag
A simplified model was used to predict the influence of temperature on the size
of fluidized particles. It assumes that a small particle adheres on a larger one if its
weight is smaller than van der Waals forces active at contact points between
particles. Accordingly, particles of different sizes stay alone or as aggregates
depending on the magnitude of cohesive and gravitational forces. Considering the
aggregate of particles suspended in
1.2
the space, the application of an
25 °C
200 °C
acoustic field may produce the break
400 °C
600 °C
0.9
up of the aggregate, when inertial
and drag forces applied to the
10 µm
80 µm
aggregate particles overcome its
0.6
cohesion. Sound affects fine/coarse
particles aggregates as results of a
0.3
relative motion between particles.
Coarse and fine particles follow gas
0.0
oscillations with an amplitude that
-9
depends on their size and on
16x10
150 dB
intensity and frequency of the
12x10-9
acoustic field. Details of the model
are reported elsewhere (21). Figure
8x10-9
2A gives the displacement of
particles of different size over gas
4x10-9
particles displacement, Adi/Ag. Adi/Ag
= 1 means that particles oscillate as
0
gas does, Adi/Ag = 0 means that
-1
0
1
2
3
4
5
10
10
10
10
10
10
10
particles are stationary in the space.
For the particles size considered,
frequency, Hz
relatively low frequencies (f<1Hz) as
Fig 2. A) Relative displacement of particles over gas
well as relatively high frequencies
particles displacement: Adi/Ag and B) maximum
(f>104 Hz) are not able to promote a
disaggregating forces and cohesive forces on a
80µm/10µm particles aggregate as a function of sound
relative motion of particles. For
frequency.
A
B
frequencies larger than 10Hz, coarse particles are fixed in the space (Adc/Ag=0) and
fine particles oscillate (0<Adf/Ag≤1).
Cohesive forces between particles counteract the relative displacement of the
particles. Coarse/fine particle detachment occurs when the disaggregating force due
to particles relative motion overcomes the cohesive forces acting at contact points.
According to Russo et al. (22), it is Fc, cohesive = nµFcw, with n number of contact points
between particles, µ static friction coefficient and Fcw van der Waals force between
particles (17). µ=0.5 (23) and n=3 have been used in calculations. The effects of
temperature has been accounted for considering that: i) gas density and viscosity
are temperature dependent (2): ρg=1.2x(293/T) and µg=146x10-6 T1.504/(T+120); ii)
temperature does not affect the density of the solid particles; iii) two alternative
considerations have been made on van der Waals forces: (A case) Fcw=cost, or (B
Case) Fcw= Fcw(T) as increasing Hamaker constant (19).
Figure 2B gives the highest value of the disaggregating forces due to the
application of a 150dB sound field acting on a 80µm/10µm particles aggregate as a
function of frequency at different temperatures. In the figure the cohesive forces
active between the small and the coarse particles are also reported as horizontal
lines. Disaggregating forces, negligible for frequencies <1Hz, first increase reaching
a maximum value and then decrease becoming negligible for frequencies >104Hz.
The increase in temperature results in an increase of the maximum disaggregating
forces of a factor of 3 and also in a moderate increase of the optimal frequency of
sound. The sound will be able to separate the aggregated particles when
disaggregating forces are larger than cohesive forces (horizontal lines). With
reference to ambient conditions (solid lines), a frequency in the range 7-300Hz is
required when an acoustic field of 150dB is applied. With reference to A case, the
disaggregating forces increase with temperature, while cohesive forces remain the
same (solid horizontal line). This results in a larger range of operative frequencies.
However, this conclusion is not fulfilled by comparing the curves of disaggregating
forces with those of cohesive forces when the latter are assumed to be temperature
dependent (B Case). In this case an increase of temperature results in a decrease
of the range of operability frequencies and at 600°C an acoustic field of 150 dB is
not able to separate the particles whatever the frequency used (dash-dot lines).
EXPERIMENTAL RESULTS
Group A material – Silica sand. Minimum fluidization velocity (umf), minimum
fluidization bed voidage (εmf), terminal velocity (ut), Richardson-Zaki exponent (n)
and average size of fluidized particles calculated by working out minimum
fluidization (dumf) or terminal velocities (dut) are reported in Fig. 3 as a function of bed
temperature. Data are obtained in tests carried out without the use of an acoustic
field (solid symbols) and under sound assisted conditions (open symbols) with
acoustic fields intensity of 150 dB and frequencies of 50, 120, 300 Hz. Also smaller
intensities of the acoustic field, 130 and 140 dB were investigated and similar results
have been obtained. Associated to a less sound intensity a smaller effects of sound
application has been found.
All the variables increase with temperature. This behaviour is not expected on
the bases of purely hydrodinamic considerations on the effect of temperature on gas
viscosity and density. The comparison among tests carried out with and without the
application of acoustic fields shows that at ambient conditions the application of
80
ut, cm/s
0 .9
0 .6
0 .3
0 .0
εmf
10 0
0
200
400
0 .6
30
0 .5
20
0 .3
0
200
4 00
0
600
15 0
15 0
12 0
12 0
t
90
n o so u n d
50 H z
3 00 H z
1 20 H z
60
30
0
0
200
400
600
0
200
400
600
10
du , µm
mf
40
0
600
0 .4
du , µm
60
20
n
umf, cm/s
1 .2
0
2 00
40 0
tem p era tu re, °C
6 00
90
n o so u n d
50 H z
300 H z
120 H z
60
30
0
0
2 00
400
6 00
tem p eratu re, °C
Fig. 3. Group A material – Silica sand. Minimum fluidization velocity, bed voidage, terminal velocity,
Richardson-Zaki exponent and average sizes of fluidized particles as a function of temperature.
sound involves a remarkable reduction of all considered variables. Increasing
temperature, there is lower and lower influence of sound application that eventually
vanishes for bed temperature of 600°C. The frequency of the acoustic field shows a
non monotonous trend: 120Hz is the most effective frequency. The value of
Richardson and Zaki exponent at ambient conditions without sound, n=20, is
relatively high and it increases up to n=30 as temperature increases up to 600°C.
Such high values of n are representative of high degrees of cohesiveness of the
material (11) and its increase with temperature indicates an increased role of
cohesive forces. The application of an acoustic field reduces n by a factor of 3,
5<n<10. The comparison among average sizes of fluidized particles calculated
working out minimum fluidization or terminal velocities shows that, whatever the
procedure used, similar values and trend are obtained. In both cases the average
sizes of fluidized particles obtained without sound are larger than the average size
of the material, 60µm. The application of sound generally reduces the size of
fluidized particles even if the effect decreases as temperature increases and
vanishes at temperature of 600°C.
With reference to the simple model presented in Theory section it must be noted
that predictions are in agreement with experimental findings. For example,
considering the powder made of only two particle sizes, 80µm and 10µm, with
relative weight fractions of 0.9 and 0.1, the model indicates the formation of 84µm
aggregates. This size is very close to those found in fluidization experiments without
sound at ambient temperature. An acoustic field of 150dB and 120Hz is able to
break up 80/10µm aggregates and this should result in the decrease of average size
of fluidized material to 60µm. The effect of an increase of temperature can be only
umf, cm/s
20
partially justified by theory when an
increase of cohesiveness of the material
15
with temperature is assumed (B Case).
10
Group B material – Silica sand.
Minimum
fluidization
velocity
(umf),
5
minimum fluidization bed voidage (εmf) and
0
average size of fluidized particles
0.6
calculated by working out minimum
fluidization velocities (dumf) are reported in
0.5
Fig. 4 as a function of bed temperature.
0.4
Analysis of figure shows that, as expected
on the basis of purely hydrodnamic
0.3
considerations,
minimum
fluidization
velocity decreases with temperature and
400
bed voidage at minimum fluidization
conditions increases. The effect of
200
no sound
temperature on average size of the
140 dB - 120 H z
fluidized particles is limited. The
0
0
200
400
600
comparison among tests carried out with
tem
perature,
°C
and without sound shows a small
reduction of all variables but no effects on Fig. 4. Group B material – Silica sand. Minimum
their trends. For instance, considering fluidization velocity, bed voidage and average
ambient temperature experiments, the sizes of fluidized particles as a function of
temperature.
average size of fluidized particles without
sound application is 410µm, while that
obtained with sound application reduces to about 300µm. Both values are close to
the average Sauter diameter, 340µm, of the material. The differences are likely to
be related to the effect of sound on the removal of some smaller particles originally
adhering on the material.
Group C material – Ashes. Minimum fluidization velocity (umf), minimum fluidization
200
400
600
0
200
400
600
mf
du , µm
εmf
0
2 .5
0 .0 9
u , cm/s
u , cm/s
2 .0
t
mf
0 .0 6
0 .0 3
1 .5
1 .0
0 .5
0 .0 0
0
200
400
600
0 .0
800
0
200
400
600
800
0
200
400
600
800
20
0 .6 5
mf
15
ε
n
0 .6 0
10
0 .5 5
0
200
400
600
d
0
30
800
20
20
ut
umf
, µm
30
d , µm
0 .5 0
5
10
0
140 dB - 100 H z
140 dB - 120 H z
0
200
400
600
te m p e r a tu r e , ° C
800
10
0
140 dB - 100 H z
140 dB - 120 H z
0
200
400
600
800
te m p e r a t u r e , ° C
Fig. 5. Group C material – Ashes. Minimum fluidization velocity, bed voidage, terminal velocity, RichardsonZaki exponent and average sizes of fluidized particles as a function of temperature.
bed voidage (εmf), terminal velocity (ut), Richardson-Zaki exponent (n) and average
size of fluidized particles calculated by working out minimum fluidization (dumf) or
terminal velocities (dut) are reported in Fig. 5 as a function of bed temperature. Data
are obtained in tests carried out only under sound assisted fluidization conditions,
SPL=140dB and f=100 and 120Hz (open Symbols) due to the impossibility of
obtaining an ordinary fluidized state. With the exception of terminal velocities, which
are relatively constant, all variables increase with temperature. 100 Hz frequency of
sound results into smaller particle size and therefore a higher effectiveness of
agglomerates breaking-up. n varies from 8 to 18 as temperature increases from
ambient to 500°C. These relatively high values are indicative of elevated degrees of
cohesiveness of material even in conditions of sound assisted fluidization.
LITERATURE CORRELATIONS PREDICTIVITY
0
(umfexp/umft-1)*100, %
(nexp/nt-1)*100, %
(utexp/utt-1)*100, %
(umfexp/umft-1)*100, %
Experimental values of minimum fluidization velocity, terminal velocity and
Richardson-Zaki exponent, obtained for the Groups A and B materials with and
without the use of acoustic fields, were compared with values predicted by available
correlations. Ergun (20), Stokes (13) and Richardson and Zaki (12) correlations
were used. Minimum fluidization velocities were calculated in two cases: i)
considering a constant value(obtained at ambient temperature) of minimum
fluidization voidage with temperature (ε0); ii) assuming for each temperature the
values of minimum fluidization voidage from experiments (5).
Figures 6 and 7 give the deviation of
εmf=ε0=const
correlations from experiments. For Group
600
εmf=εmf(T)exp
A material, without sound (solid symbols),
εmf=ε0=const
400
deviations of correlations increase with
εmf=εmf(T)exp
temperature up to deviations as high as
200
400%-500%. Accounting for temperature
effects on minimum fluidization voidage
0
there is a strong effect on minimum
fluidization velocity predictions whose
600
deviations are reduced. Deviation are
smaller if data from sound assisted
400
fluidization experiments (open symbols)
are considered. The reduction of
200
interparticles
forces
increases
the
600
400
200
0
0
200
400
600
temperature, °C
Fig. 6 Group A material – Silica sand. Deviation
of Ergun (20), Stokes (13) and Richardson and
Zaki (12) correlations from experiments.
100
εmf=ε0=const
80
εmf=εmf(T)exp
60
40
20
0
0
200
400
600
temperature, °C
Fig.7 Group B material – Silica sand. Deviation of Ergun
(20) correlation from experiments.
predictivity of the correlations. This effect is rather limited for terminal velocities but it
must be considered that relatively large uncertainties are due to the extrapolation of
bed expansion curves. For Group B material, predictions of minimum fluidization
velocity is rather good, deviations smaller than 20%, especially when accounting for
temperature effects on minimum fluidization voidage.
CONCLUSIONS
•
•
•
•
•
The influence of temperature on fluidization has been investigated for three
materials of Groups A, B and C of Geldart classification. The behaviour of
group A and C powders can hardly be explained on a purely hydrodynamic
basis on the effect of temperature on gas viscosity and density.
The different role played by interparticle forces on fluidization of Group A, B
and C powders has been highlighted by comparing experimental findings in
ordinary and sound assisted fluidization.
Deviations of literature correlations for Group A material are relatively high and
increase with temperature. These decrease when cohesive forces diminish.
Literature correlations are suitable for Group B material especially when
accounting for temperature effects on minimum fluidization voidage.
A simple model has been presented to account for the role played by van der
Waals forces on the size of fluidized particles in the case of multi-sizes Group
A powders. The model can account for temperature effects on both
hydrodynamic and cohesive forces.
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