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A particle population balancing model for a circulating fluidized bed
combustion system
K. Redemann, E.-U. Hartge, Joachim Werther
Institute of Solids Process Engineering and Particle Technology, Hamburg University of Technology, Denickestr. 15, D-21071 Hamburg, Germany
a b s t r a c ta r t i c l e i n f o
Article history:
Received 4 September 2007
Received in revised form 15 August 2008
Accepted 23 September 2008
Available online 1 October 2008
Keywords:
Particle population balance
Circulating fluidized bed
Fluid dynamics
Refuse derived fuel
A dynamic simulation model of the particle population in a circulating fluidized bed combustor with external
heat exchanger has been developed. It considers the fluid dynamic processes in the various parts of the
system, as well as the particle attrition. To handle multiple solids types simultaneously and to fulfill the mass
balances, some of the fluid dynamic sub-models taken from the literature were modified. The model allows
to calculate the solids mass flows as well as the corresponding particle size distributions at any point inside
the combustion system.
The model has been applied to the combustion plant of Stadtwerke Neumnster in Germany, which operates
on refuse-derived fuel. The particle balancing model provides new insights into the operating behavior of
such a system. In particular, the calculation of the residence time of different particle classes in the system
reveals a very broad distribution of size dependent average residence times, ranging from several minutes to
a maximum of roughly 40 h. A size fraction exists between 100 and 300 m with a maximum average
residence time of about 40 h. The Preprint submitted to Elsevier Science 15 August 2008 simulation provides
a means for examining possibilities to control the particle size distribution in the combustion system. It is
shown how a recirculation of a fine ash fraction can be used to control the bed particle size distribution in the
combustion chamber.
2008 Elsevier B.V. All rights reserved.
1. Introduction
A key parameter for the proper operation of a circulating fluidized
bed combustor (CFBC) is the particle size distribution (PSD) of the bed
inventory.
It governs e.g. the solids circulation rate and with it the heat
transport from the combustion chamber into the external heat
exchanger. The particle population results from the PSDs and mass
flows of the solids fed into the system and reaction, classification,
transport and comminution processes occurring in the plant.
Improper operating conditions or imperfect plant components cancause serious problems in the plant operation.
For example, the separation behavior of the cyclone, which is
attached to the combustion chamber, is a major issue. A properly
designed cyclone should be able to keep a given mass of solids with a
predetermined particle size distribution in the cycle. If the loss of
material through the cyclone is too high and if the input of fresh ash
for example in the case of a coal with a low content of ash is too
small, it may be necessary to continuously add new bed material, in
order to keep the mass of solids in the inventory. Respective operating
experience exists with Rheinbraun [1].
It is thereforedesirable to have a properly designed cyclone,whose
design is considering the special operating conditions in CFB
operation, i.e. the high solids loading at the inlet. Comprehensive
work on the design of cyclones under these conditions, which was
mainly focused on the inlet design and the formation and flow of the
strand formed there, has been carried out by Muschelknautz and his
group at the University Stuttgart (e.g. [24]) and by Reh and his co-
workers at ETH Zrich (e.g. [5,6]). Their results have found a striking
confirmation by the experience made by Alstom in their Zeran project
[7]. The Zeran A boiler in Warsaw, Poland, a 450 t/h CFB steam
generator, was commissioned in 1995. At that time it was the largestCFB boiler in Poland and the first to operate on Polish hardcoal. Due to
the high debris rock content in the ash it turned out to be difficult to
achieve the proper particle size distribution of the circulating ash. The
cyclones were not able to prevent the loss offine inert material. When
the order for the boiler B of Zeran was placed in 1998, it was built
almost identical to boiler A, with the exception of the cyclone design.
In order to improve the separation efficiency the arrangement of the
cyclone's inlet ducts with respect to the furnace was optimized, the
inlet ducts were prolonged and inclined downward, the vertical
velocity in the cyclone was decreased and eccentric vortex finders
were installed.
The new design turned out to be extremely efficient: the 50% value
of the cumulative mass distribution of the circulating particles went
down from 180 m for boiler A to 75 m for boiler B. The increased
Powder Technology 191 (2009) 7890
Corresponding author. Tel.: +49 40 42878 3239; fax: +49 40 42878 2678.
0032-5910/$ see front matter 2008 Elsevier B.V. All rights reserved.
doi:10.1016/j.powtec.2008.09.009
Contents lists available at ScienceDirect
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cyclone efficiency and the thus realized finer inventory of the system
had several beneficial effects, including an increased overall heat
transfer coefficient, which allowed to reduce theinventoryand thus to
lower power consumption. Furthermore limestone utilization was
improved and even the NOx and CO emissions were reduced.
It is interesting to note in this context that the same experience
with regard to the significance of the cyclone design was made over10 years before in Germany [8]. Two 105 MWth CFB boilers were built
for Bayer AG on their Leverkusen site. Thefirst one was commissioned
in 1988, thesecond onein 1991. Duringoperation (both units operated
on the same coal) it turned out that in the second unit the combustion
efficiency was lower, the Ca/S ratio was twice as high, the dp,50 of the
recirculating ash was 170 m instead of 150 m and the fly ash had a
dp,50 of 80 m compared to 30 m in the first unit. A detailed analysis
brought the result that the cyclone design had been changed
unintentionally, i.e. the diameter of the vortex finder had been
increasedby 14% anda designchange of thevortexfinder's suspension
enabled a short-circuiting flow to take place.
The PSD of the bed inventory results from the fluid dynamic
processes in the different plant components, the ash formation
behavior of the fuel and additionally fed solids, e.g. additional inertsolids, limestone or recycled bed material. A mathematical simulation
tool considering these effects can be used to predict the PSDs in the
different parts of a circulating fluidized bed under various operating
conditions. It can also be used to survey and judge the impact of
changes in theoperation of a plant or in thecharacteristicsof theinput
fuel on the resulting particle size distributions.
In the present work a mathematical model based on particle
population balances is developed, which considers the circulating
fluidized bed combustion system as separate modules. Mathematical
descriptions were, as far as possible, taken from the literature.
However, in some cases available descriptions had to be modified in
order to fulfill the requirements of particle population balancing. The
resulting model represents a dynamical description of the system
behavior, which also allows conclusions about the residence time of
individual size fractions in the system to be drawn.
The model is first applied to the simulation of the refuse-derived
fuel fired circulating fluidized bed combustor of Stadtwerke Neumn-
ster GmbH in Neumnster in north Germany. Its schematic layout is
shown in Fig. 1. Refuse-derived fuel (RDF) is fed into the combustion
chamber. Fly ash is leaving via the cyclone overflow and is collected in
the heat recovery boiler and the multi-cyclone. Finally small quantities
of ultra fine ash are passing into the flue gas treatment section.Since the ash particle size distribution which is produced by the
refuse-derived fuel cannot be easily predicted, the plant contains two
means for influencing the PSD of the bed inventory. The one is the
addition of sand, which was also used for starting the facility. The
second means is the recirculation offine ash, obtained after sieving of
the bottom ash offtake.
In the framework of a research project initiated by Stadtwerke
Neumnster, measurement campaigns were carried out where solids
mass flows and solids particle size distributions were measured at
different locations at the plant. Additional lab scale investigations
formed the basis for the development of the particle population
balances presented here. Since the experimental facts were decisive
for the design of the model, they will be presented below before the
description of the theory.
2. Experimental
2.1. Measurements at the Neumnster plant
In general measurements of solids mass flows and solids particle
size distributions in an industrial plant arequite difficult. Theaccess to
the various parts of such a complex system is not easy, safety
precautions have to be taken and above all, the refuse-derivedfuel is a
matter which is very difficult to characterize.
Solids mass flows were determined on larger time intervals by
counting the number and loading of trucks which transported the
ashes to a disposal site. This was done for the coarse bottom ash, the
fine bottom ash, the fly ash (sum of ashes taken from the radiation
boiler, convection boiler and the multi-cyclone). The sand supply was
Fig. 1. Flowsheet of a circulating fluidized bed combustion system (Neumnster plant).
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also measured. It is admitted that all flows necessarily contain sand
particles as well, so all ash streams are in reality mixtures of fuel ash
and sand. However, for simplicity these streams are still called ashhere. The mass flow of the ultra-fine ash was calculated from
information about the lime and activated coke fed to the flue gas
cleaning andabout the solidswithdrawn from theflue gas cleaning for
disposal. From these information the ash input with the refuse-
derived fuel could be calculated.
With regard to the solids particle size distributions samples were
taken of the coarse bottom ash, the fine bottom ash, the fly ash
(mixture offly ashes taken from the different sources) and from the
sand. The solids samples were analyzed by sieving and a laser
diffractometer (Beckman-Coulter LS 13 320). No sample could be
taken from the ultra-fine ash. For this latter material the correspond-
ing particle size distribution was estimated by calculating the
separation efficiency of the multi-cyclone for the given fly ash. Fig. 2
shows the particle size distributions of different samples and Table 1presents the measured solids mass flows.
2.2. Measurement of the attrition characteristics of the refuse-derived
fuel ash
The RDF which is used in the Neumnster plant is produced by
mechanical and biological processing of the municipal waste from
the north German region around Neumnster. The processing plant
has a total capacity of 210,000 t/h of household waste. It produces
103,000 t/h refuse-derived fuel. The processing results in an increase
of the calorific value of 9 MJ/kg for the original waste to 14.5 MJ/kg of
the RDF. The RDF itself is very difficult to characterize.
It contains pieces of wood and organic matter, as well as sheets of
paper and plastics. The
particles
have a maximum dimension ofroughly 10 cm. According to the concept of the primary ash particle
size distribution (PAPSD) suggested by Salatino and co-workers [9,10],
devolatilization and combustion of a solid fuel leads to an ash particle
size distribution, i.e. the PAPSD, which will during its further residence
time in the combustion chamber undergo fragmentation and attrition.
For population balancing purposes it is necessary to follow the
changes of particle sizes inside the combustion system. In previouswork on the modeling offluid bed catalytic reactors [11] and coal and
sludge combustion in the fluidized bed [12], the authors' group has
developed a tool for the description of attrition processes. In order to
apply the same tools to the RDF combustion problem, samples of the
original RDF were exposed for a short time to combustion conditions
in a fluidized bed in order to create an ash sample, which could then
be further used.
Fig. 3 gives an example of sucha distribution. Of course this is not a
real PAPSD in the sense of its definition, because it has already
undergone some stress in the fluidized bed due to the finite residence
time under combustion conditions. However, the material is well
suited for attrition experiments.
Following the distinction of the three attrition mechanisms [13]:
in-bed attrition by solids movement, induced by bubbles in-bed attrition, induced by distributor jet action
attrition during the passage through a cyclone
the attrition characteristicswere determinedin specialized testfacilities,
which have been described elsewhere [13].
Fig. 4 shows two sets of data for the bubble induced attrition. The
attrition rate r in kg of fines produced per kg of bed material and
second is plotted against the time. It is remarkable that contrary to
what was observed with catalyst and coal ashes [13] no constant
attrition rate is obtained after a certain time of operation. Obviously,
due to the structure of the RDF ash no steady-state attrition rate is
reached. On the contrary, the particles are continuously breaking
down and even after 1500 h of attrition no plateau is reached.
Fig. 2. Measured particle size distribution of ashes leaving the plant and of the feed
sand.
Table 1
Measured solids mass flows and calculated feed mass flow of attrited ash at the
Neumnster plant
Solids stream Mass flow
[kg/h]
Ultra fine ash 481
Fly ash 1778
Fine ash 1508
Coarse ash 1390Sand 373
Feed of attrited ash 4786
Fig. 3. Measured PAPSD originating from laboratory scale fluidized bed combustion.
Fig. 4. Results for bubble induced attrition experiments with two different ash samples,
operated at a superficial velocity of u =0.5 m/s, plotted against the operating time.
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In Fig. 5 the attrition rate r is plotted against the relative material
loss matt/ mb0, where matt denotes the cumulative attrited mass and
mb0 is the initial bed solids mass. Both experiments can beapproximated by straight lines on the semi-logarithmic grid,
r a exp b mattmb0
& ': 1
The different slopes are probably due to the fact that both ashes
originate from different RDF samples.
Fig. 6 shows in its upper half the time-dependent attrition rate in
kg of attrited material produced per time unit for the jet attrition test,
as a function of time. Again, no steady state of attrition is reached. In
the lower half the attrition rate is plotted against the relative material
loss matt/mb0. Fig. 7 shows the results of the cyclone attrition test for
two different samples operated under different conditions. Here also,
no steady state attrition is reached.
3. Theory
3.1. The particle population balancing model
Although Fig. 1 presents a special design of a circulating fluidized
bed combustion system the model, which is presented here, can be
applied to any other circulating fluidized bed combustor design. The
aim of the mathematical model is to track the particle population in
the bed inventory of a CFBC. The software tool calculates the physical
processes in a dynamic-sequential simulation with a pipe-and-filter
architecture [14].
The simulation model divides the CFB system into modules, each
representing an apparatus of the plant. The combustion chamber is
separated into two sub-modules, the dense bottom zone and the
upper dilute zone. The calculation of transport, classification and
comminution of the solids in the different parts of the plant isperformed in these modules. They are calculated sequentially in the
order the solids are passing them. An overview of the whole model
setup is given in Fig. 8.
Although a lot of more sophisticated models are available for the
description of the fluid mechanics of circulating fluidized beds (e.g.
[15]) a very simple approach is followed here, where the circulating
fluidized bed is modeled as a bubbling fluidized bed, operated at high
gas velocities with a correspondingly high solids elutriation. Therefore
above a dense bottom zone which contains the bubblingfluidized bed
and where the accumulation of solids is considered, we have a
freeboard section with solids transport and segregation with height.
In the cyclone the separation is considered and transport in the
return leg. The external heat exchanger is treated simply as a stirred
Fig. 5. Results for bubble induced attrition experiments for with different ash samples,
operatedat a superficial velocityofu =0.5 m/s, plotted against therelative mass loss due
to attrition.
Fig. 6. Resultsfor jetattritionexperiments, operated at a superficialvelocityofu=0.5 m/s,
jet velocity ofuj=50 m/s, nozzle diameter do=1 mm, ds=189 m plotted against time and
against the relative mass loss due to attrition.
Fig. 7. Results for cyclone attrition experiments for with different ash samples, operated
at different operating conditions (cyclone diameter: 90 mm, further details cf. [31]).
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tank with regard to the solids. Accumulation is taken into account, butno entrainment with the fluidizing gas. The entrainment may be
neglected, since entrained fines are fed again to the combustion
chamber together with the off-gas from the EHE.
The devolatilization and combustion times of the fuel particles are
in the order of seconds to minutes [16]. On the other hand the
residence times of ash particles in the system are of the order of
minutes to hours, as will be shown below. Therefore as a means of
simplification the combustion is placed outside the combustion
chamber and only ash with its primary ash particle size distribution
(PAPSD) is entering into the combustion chamber. The ash particles
are then undergoing bubble-induced attrition and jet attrition in both,
the dense bottomzone of the combustion chamber andin the external
heat exchanger. Furthermore attrition is occurring in the cyclone.
In CFBCs various solid types, e.g. fuel ash, sorbent material or
additional inert material, are present. These solids have different
physical properties, e.g. densities and particle sizes, which are
influencing the particle behavior in the fluidized bed system. Another
important parameter is the stress history of the particles (e.g. [11,12]).
In order to map all of these effects, the model treats particles of
different size, solid type andstress history separately. For that purpose
the bed inventory is discretized into a three dimensional matrix,
which contains classes of particles with the same combination of the
three characteristic properties, mentioned above. As proposed by
Scarlett [17], the matrix entries contain the masses in the respective
particle classes. All other characteristic values, e.g. the Sauter diameter
and the minimum fluidizing velocity are derived from that matrix.
3.1.1. Modeling of the combustion chamber
The combustion chamber module is divided into two sub-modules,the dense bottom zone and the upper dilute zone. The dense bottom
zone is modeled as a bubbling fluidized bed with an approach
according to Werther and Wein [18] and the upper dilute zone is
described according to Kunii and Levenspiel [19]. Both sub-modules
calculate the vertical solids volume profile. Solids are elutriated from
the dense bottom zone into the upper dilute zone, whereby the
masses of the particles classes in the upper dilute zone result from the
PSD in thedensebottom zone. Thetask of combustion chamber model
is to find the mass and PSD in the dense bottom zone with which the
mass balance in the total combustion chamber if fulfilled. This is
achieved in an iterative calculation process.
3.1.1.1. Modeling the dense bottom zone. The Werther and Wein
model [18] was used to calculate the vertical profile of the solidsvolume concentration in the dense bottom zone. To handle conical
shapes of the combustion chamber, thewideningof the cross-sectional
area with height is considered forthe calculation of themasses andthe
pressure drop in the dense bottom zone.
From the overall solids volume concentration cv at height h above
the gas distributor and the height of a suspension layer h, the solid
mass of the layer m can be calculated by
m A h s cv h h 2
where s is the solid and A(h) the cross-sectional area of the dense
bottom zone at the height h.
The pressure drop pb of the dense bottom zone can be calculated
from
pb sZhb
0
A h cv h dh 3
where hb denotes the height of the dense bottom zone.
3.1.1.2. Elutriation into the upper dilute zone. The mass elutriated
from the particle fraction i into the freeboard per time unit is given by
:mi
K4i
Q3;i
A
4
where Q3,i is the mass fraction in the dense bottom zone and A the
cross-sectional area of the combustion chamber at the height hb above
the distributor. The elutriation constant Ki is a key parameter for the
modeling of the upper dilute zone. A correlation for Ki was developed
by Colakyan and Levenspiel [20] for gas-particle systems at operating
conditions comparable to the conditions found in CFBCs. Unfortu-
nately, this elutriation model assumes that particles with a terminal
velocity ut exceeding the superficial velocity u cannot be elutriated.
The measurements taken in the Neumnster plant, which will be
described later on, have shown that this is not the case in a circulating
fluidized bed. We have found a considerable amountof particlesin the
external heat exchanger ash with sizes corresponding to terminal
velocities exceeding the operating gas velocity in the upper dilute
zone of the combustion chamber. Therefore a correction factor fKwithvalues between 0 and 1 was introduced into the Colakyan and
Levenspiel correlation,
K4i 0:011 s 1ut;i fK
u
2for ut;i fKb u
K4i 0 for ut;i fKz u5
where the solids density s is to be inserted in kg/m3. ut,i is the
terminal velocity of the particle class i. The effect of the factor fk is
shown in Fig. 9. The factor shifts the curve of the elutriation rate to the
right, towards higher terminal velocities. It follows for the solids
Fig. 8. General model layout.
Fig. 9. Elutriation rate calculated from the modified Colakyan and Levenspiel [20]
model, Eq. (5), for various values of fk (calculated with s=2350 kg/m3).
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concentration above the transport disengaging height (TDH) which is
due to the particle class i
c4V;i K4i
s u ut;i fK : 6
The vertical solids volume profile in the upper dilute zone is
describedby the exponential decayapproach (Kunii and Levenspiel [19]),
cv h V c4v cvdc4v
eh V 7
where cvd isthe solidsvolume concentration at thesurfaceof thebed and
cv(h) the solids concentration at the height h above the dense bottom
zone. The decay constant is obtained from Kunii and Levenspiel [19],
u8
8
:
me;i cvi hf u ut;i fK s 9where hf is the distance between the surface of the dense bottom zone
and the middle of the inlet duct into the gas cyclone.
3.1.2. Modeling of the gas cyclone
For the calculation of the solids separation in the gas cyclone the
model of Muschelknautz [21], with themodifications by Muschelknautz
and Trefz [22] has been taken as a basis. In this model the separation
mechanismin the cyclone is divided into twoparts.At first, immediately
near the inlet that part of thesolids loadinge, which exceeds a limiting
valueg is forming a strand, whichflowsdirectly into theunderflow.The
remaining part of the solids is undergoing the separation in the vortex.
Both mechanisms are described by semi-empirical correlations, which
arebased on a large numberof measurements, including measurements
at large-scale industrial cyclones.Unfortunately,the Muschelknautz model doesnot fulfill the fractional
solidsmass balances forthe calculationof thestrand separation, which is
a crucial point fora particlepopulation balancingmodel. Also mixtures of
solids with different densities and particle size distributions have to be
considered in the present application. Therefore the Muschelknautz
model had to be modified.
3.1.2.1. Modeling the strand separation. Under the conditions prevail-
ing in circulating fluidized bed combustors the solids loading e at thecyclone inlet exceeds the loading limitg by far [6]. Therefore the strand
separation is responsible for most of the cyclone's separation efficiency.
Theparticleattribute which is decisive forthe separation in a gascyclone
isnot its sizebut rather its terminalvelocity. In order to beableto handle
mixtures of solids of different sizes and densities the terminal velocity is
chosen here as the quantity which unambiguously characterizes a given
particle with respect to its separation in the cyclone. The particle size
distributions of mixtures of solids of different densities are therefore
converted into a single distribution of terminal velocities ut.
Particles with a probability of 50% to be separated in the strand
have according to [21] a terminal velocity of
ws;50
0:5 0:9
:Ve
Aw 10
where Ve is the inlet gas volumeflowandAw is the sedimentation area
of the strand, defined in [21].
The loading limit g can by calculated from
g Kg4ffiffiffiffiffiffiffiffiffiffiffiffi
ws;50ut;50;e
s 10e k 11
The exponent k in Eq. (11) can be calculated by
k 0:15 0:66 exp e0:015
0:6 !12
ut,50,e is the50% valueof the terminalvelocity distributionof the solids
mixture entering the cyclone.In the original Muschelknautz model [21] the particle size
distribution of the solids going into the inner vortex is described by
Fig.10. Comparisonof theinner feedPSDs and separation efficiency curves calculated fromthe Muschelknautzand thenew model forthe strand separation in a laboratory cyclone(a,
b) and the large cyclone of the Neumnster plant (case c).
83K. Redemann et al. / Powder Technology 191 (2009) 7890
where u is to be inserted in [m/s]. The mass flow in the particle class
i (me,i) leaving the combustion chamber can be calculated with the
particle slip velocity
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a RRSB distribution. The assumption of this distribution leads to a
violation of the mass balance, because the RRSB distribution implies
the presence of particle sizes which need not exist in reality. To
circumvent this problem, the assumption of the RRSB distribution for
the inner feed material hasbeen replaced here by modeling the strand
separation with a separation efficiency function.
The mean terminal velocity of the particles entering the inner
vortex, ut,50,v is then in analogy to [22] calculated from
ut;50;v ut;50;e for e Vgut;50;v ffiffiffiffiffiffiffiffiffiffiffiffiut;50;ep ffiffiffiffiffiffiffiffiffiffiffiffiut;50;ep ffiffiffiffiffiffiffiffiffiffiffiws;50p 1g=e
0:75
2for g be V 4 g
ut;50;v ws;50 for e N 4 g
:
13
Using this terminal velocity the function for the strand separation
efficiency can be set up in analogy to the approach by Rogers [23],
T ut 1a T4 ut a 14
with
T4 ut
1
1 ffiffiffiffiffiffiffiffiffi
ut;50;vut
q exp 1
ffiffiffiffiffiffiffiffiffiut
ut;50;v
q3
!& ' ; 0 V T4 V 1 15where is the separation sharpness and a is an offset value.
The total solids mass flow m v into the vortex, the so-called inner
feed is prescribed by the solids loading limit g of the gas and its mass
flow. To comply with the loading limit, the inner feed is fitted by
means of the offset value a in Eq. (14). It adjusts the mass flow of the
solids going to the inner vortex, but leaves the PSD of this material
unchanged. It is calculated by
a i T4 ut;i :me;ig 0:9 :Ve s
i
T4 ut;i :me;i : 16
There are cases possible, where the total mass in the particleclasses with T(ut)b1 is too small to fulfill the required loading limit.
This will then lead to negative values of a with Eq. (16). For these
exceptional cases, the directive given in Eq. (13) is neglected and the
mean terminal velocity ut,50,v is raised until the loading limit is
fulfilled with an offset of a = 0.
The mass flow m v, i of a particle class i entering the inner vortex is
calculated from the massflow of theparticleclass entering thecyclone
m e,i, multiplied with the corresponding separation efficiency.
:mv;i 1T ut;i
:me;i: 17To estimate the impact of the changes made to the strand
separation model, three different cases were calculated with the
original model given in [21] and with the new model discussed above.
In Fig. 10 the results are compared.
In cases A and B laboratory cyclones were simulated with two
different feedparticle sizedistributions at the sameloadinglimite=0.05.
The geometry of the cyclone and the operating conditions are given
together with the calculation parameters values in Table 2. In case C a
large-scale cyclone with the dimensions and operating conditions of the
Neumnster plant has been chosen. Its dimensions and operating data
are also listed inTable 2. The most significant distinction between cases A
and B on the one side and case C on the other side is the high solidsloading ofg=8 in the latter case.
In addition to theinlet PSDs and thecalculated inner feed PSDs, the
separation efficiency curves according to the original model and the
new model are depicted in Fig. 10. The separation efficiency of the
original model [21] has been calculated from the ratio of the predicted
inner feed PSD to the corresponding mass fraction in the cyclone inlet.
In all cases the separation sharpness used in Eq. (15) was = 0.05. The
offset a has been calculated from Eq. (16).
It can be taken from Fig. 10 that the separation efficiency curves
calculated with the present model are practically identical with those
derived from the Muschelknautz model. The advantage of the present
model is that it does not violate the fractional mass balances and
therefore can be used for population balancing.
3.1.2.2. The separation in the inner vortex. The particle diameter dv
with force equilibrium on the radius with the maximum vortex
velocity can be calculated according to [21]
d4v ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
18L0:9:Ve
sg
u2i 2hi
vuut 18
where Ve is the volumetric gas flow entering the cyclone, L the
dynamic viscosity of the gas, g and s the densities of gas and solids,
respectively, hi is the distance between the vortex finder and the apex
and ui the maximum tangential gas velocity. According to Eq. (18)
Table 2
Cyclone dimensions, suspension and model parameters and intermediate results of the
strand separation calculation for three different cyclone arrangements, carried out with
the Muschelknautz [21] and the present model
Parameter Unit Cases
A B C
Cyclonedimensions
Inlet width [mm] 13 13 1890Inlet height [mm] 37 37 4240
Outer diameter [mm] 90 90 6020
Total height [mm] 140 140 14710
Cylinder height [mm] 42 42 6464
Vortex finder dia. [mm] 28 28 1325
Vortex finder height [mm] 41 41 1065
Apex diameter [mm] 34 34 1010
Suspension Solids density [kg/m3] 2500 2500 2500
Gas density [kg/m3] 1.2 1.2 0.3
Dynamic gas viscosit y [Pa s] 18.2E6 18.2E6 46.8E6
Inlet velocity [m/s] 16.6 16.6 15.6
Solid loading [] 0.1 0.1 8
Wall friction coefficient 0 [] 0.005 0.005 0.005
Factor in Eq. (11) Kg [] 0.025 0.025 0.025
Intermediate
results
Mean inlet terminal vel. ws,50 [m/s] 0.151 0.151 0.301
Mean inlet particle dia. de [m] 19 76 76
Exponent for loading limit k [] 0.179 0.179 0.150
Loading limit g [] 1.69E3 4.22E4 1.96E2
Strand separation sharpness [] 0.05 0.05 0.05
Offset value a [] 0.632 0.323 0.991
Fig. 11. Simplified model layout, using the attrited ash particle size distribution as the
fuel ash PSD entering the system.
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solids with different densities have different vortex separation cut
sizes dv. These cut sizes are used to calculate the vortex separation
efficiency F according to [21],
F dp 0:5 1 cos 1 log
dpd4v logD
2logD
0@ 1A24 350@ 1A: 19The parameter D is discussed in [21] and can be used for the fitting
of the separation efficiency curve of a given cyclone. In cases where
solids with different densities are present in the cyclone, different
separation efficiencies for the same particle size apply due to the
different separation cut sizes. F is then a function of both dp and s.
The mass flow of a particle class (same size, same density) going
into the cyclone overflow m Ov,i results from
:mOv;i F dp;s
:mv;i 20where m
v,idenotes the solids mass flow of particle class i entering the
inner vortex.
3.1.3. Modeling of return leg and bed material bunker
Both, the return leg and the bed material bunker are modeled as
pipes with plug flow behavior and have a constant total mass. The
solids leaving the bed material bunker are fed into the bottom zone of
the combustion chamber. The solids leaving the return leg are split
into two material streams, one going directly back to the combustion
chamber and one going to the external heat exchanger.
3.1.4. Modeling of the external heat exchanger
The external heat exchanger (EHE) is modeled as a stirred tank.
Particles in the EHE are exposed to jet and bubble induced attrition,
when comminution processes are considered. As a simplification the
existence of the freeboard with its entrainment and classification
effects is neglected.
3.1.5. Modeling of the solids recycle loop
Part of the bottom ash can be recycled after removing the coarseparticles on a sieve. In the simulation the total solids mass in the bed
material silo is kept constant. The solids mass needed to be drained
fromthe combustion chamber to generatethe recyclemassflowoffine
ash can be calculated from the PSD in the dense bottom zone and the
separation efficiency curve of the sieve which is modeled according to
Rogers [23]. The model parameters arederived form the split between
the fine and coarse ash measured at the technical plant.
3.2. Modeling the attrition
The comminution processes of ashes in CFBCs can be divided into
fragmentation and attrition. Fragmentation is the breakage of a
mother particle into two or more pieces, which leads to a broader and
finer PSD. Attrition is the abrasion of small particles from a much
larger mother particle, making the mother particle shrinks slowly [13].
Abrasion is the dominant mechanism for catalysts in fluidized bed
chemical reactors [13]. As a first approximation it is assumed that the
same mechanism generally holds also for the ash particles in fluidized
bed combustion.
For the population balance expressions are required for the fines
production, on the one hand per unit time for in-bed attrition induced
by bubbles and grid jets, respectively, and on the other hand per pass
in the case of attrition in the cyclone.
The experiments described in Section 2.2 above have shown that
the rate of bubble induced attrition rb(t) is described by Eq. (1). rb is
defined as the ratio offines produced due to attrition matt to the
product of the bed mass at the time t, mb(t) and the time interval t.
rb t mattmb t t: 21
Among the factors influencing the bubble induced attrition are the
most important ones theexcess gas velocity (uumf) and the diameter
of the particle size fraction under consideration. Since no systematic
investigation of these parameters has been carried out in the present
work it is assumed according to Merrick and Highley [24], Arena et al.
[25] and Pis et al. [26],
rb~ uumf : 22
Furthermore, according to Ray et al. [27], Donsi et al. [28] and
Chirone et al. [29] it holds
rb~1
dp: 23
Fig. 12. Overview of the solids streams entering and leaving the circulating fluidized bed combustion plant.
Fig.13. Measured particle size distributions of ashes leaving the plant, the sand and the
calculated AAPSD.
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Since the dependence of the attrition rate on time twas found to
be described by Eq. (1), as a first assumption it is now assumed that
the attrition rate rb(t) is given by
rb t Kb uumf
dp exp bb
matt t mb0
& '24
where Kb and bb are material specific constants.
For grid jet attrition we are in the same situation: The influencing
parameters particle size dp, orifice diameter dor and jet velocity uorhave not been systematically varied in the present work. Therefore we
adopt the findings by Werther and Xi [30], who found that
rj~dp g d2or u3or: 25
Although the description of the time-dependence with an
exponential function is not as good as in the case of bubble-induced
attrition, we formulate
rj t Kj dp g d2or u3or exp bj matt t
mb0
& ': 26
The attrition in the cyclone occurs during the passage of the solids.
The cyclone attrition rate is therefore defined as the ratio of the mass
offines matt(n) produced during the nth passage to the mass of the
solids passing through the cyclone in this passage. According to the
experimental results in Section 2.2, rc is also described by an
exponential function. The governing parameters according to Reppen-
hagen and Werther [13] for cyclone attrition are the solids loading at
the cyclone entry e, the inlet velocity uc,in and the particle size dp.
With the same reasoning that was used above in the derivation of
Eqs. (24) and (26) the relationship determined by Reppenhagen and
Werther [13] is adapted here, which leads to
rc t Kc dp u2c;in
ffiffiffiffiffie
p exp bc matt t mc0;in
& '27
where mc0,in is the mass of the solids batch at the beginning of the setof experiments.
With the population balances the unsteady state changes in the
various parts of the fluidized bed system are monitored. For the
description of what happens during a given time interval in a given
part of the system with regard to attrition an information about the
stress history which the particle have previously undergone is
required. How far is a given particle fraction already attrited?
In previous work (Klett et al. [11]) on the time-dependence of ash
particle attrition in fluidized bed systems a stress history parameter
was used. This latter parameter basically indicates how far a given
particle is away fromthe steady stateof attrition.Unfortunately, for the
present RDFash such a steadystate is notreached, as hasbeenfoundin
the experiments described above. Therefore another description has to
be found. It is suggested now to characterize the state of the stresshistory by calculating the ratio of the mass offines matt produced
from the beginning of the attrition process, to the initial mass of the
same particle fraction m0. is taken as an indication of the amount of
stress the particle has already experienced,
mattm0
: 28
The mass offines matt can either result from the time-dependent
attrition induced by bubbles and grid jets, or from the attrition in the
cyclone, which is dependent on the number of passes or a successive
mixture of these mechanisms.
The particle population balancing calculation proceeds sequen-
tially from one module of the system to another. At the beginning of
each time-interval in a given module, the particle class i indicates itsstatus of the stress history by the mass of attrited fines matt,i, which
have originated from this particle class since its introduction into the
system, divided by the original mass m0,i. For this value ofthe actual
amountof attrition, which is occurring in the givenmodule duringthe
time-intervalt, can then be calculated as the product of attrition rate
and time-interval t, with the attrition rate being given either by
Eq. (24), (26) or (27), respectively.
3.3. The AAPSD concept
Upon entering the combustion chamber the fuel particles will be
heated and dried. Then they will devolatilize until finally the
Fig.14. Development with time of the mean particle diameter in the dense bottom zone
of the combustion chamber, the external heat exchanger and the cyclone overflow.
Fig.15. Comparison of the measured values of the pressure profile and the profile of the solids volume concentration with steadystate calculation results for the 100% load operating
conditions at the Neumnster plant.
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carbonaceous matrix is burnt out leaving the primary ash behind. Thisprimary ash will then undergo fragmentation and attrition. The
determination of the primary ash particle size distribution (PAPSD)
and of its attrition characteristics is quite difficult. The question is
whether it is absolutely necessary to consider the ash fragmentation
and attrition processes inside the combustion system, when aiming at
the population balancing of the CFB system as a whole. In this respect
a comparison of the mean residence time of the ash particles in the
combustion system with the burnout time of coal particles in a
fluidized bed combustor can be helpful.
If we take the conditions of the Neumnster plant, we have an solids
inventory in the combustion chamber of 43 t, in the external heat
exchanger of 23 t and in the return line of 6 t, whichyields a total solids
inventory of 72t. Considering thetotal ash inputof 4.8 t/hand of sand of
0.8 t/h we obtain a total solids flux of 5.6 t/h, which leads a to mean
residence time of the solids in the system of roughly 13 h. On the other
hand the burnout time of coal particles with 13 mm in afluidized bed
combustoris between 1 and10 minaccordingto La Nauze [16].Ifwetake
into account that most of thefragmentation andattritionoccurs with the
fresh ash particles, this may be taken as a justification to neglect in a
first approximation ash formation, fragmentation and attrition influ-
ences in the calculation of the particle population balances for the
fluidized bed system. This simplified model of the fluidized bed
combustor is shown in Fig. 11, which now shifts the ash formation,
fragmentation and attrition effects out of the combustion chamber such
that attrited ash only is entering the combustor. This simplified model
canonlybe used forcases as theone treated here, wherethe ashparticles
do not or onlynegligibly changethere size for most of the time theystay
in the system. In cases where larger primary ash particles shrink over a
long period and are carried out as fines only, this concept would fail.From Fig.12 it follows that thefollowing mass balance holds for the
integral mass flow
:mAA :muf
:mfly
:mcoarse :mfine
:msand: 29
However, the analogous balance also holds for the particle size
class i
:mAA;i
:muf;i
:mfly;i
:mcoarse;i
:mfine;i
:msand;i: 30
4. Results and discussion
4.1. Determination of the attrited ash particle size distribution (AAPSD)
In the first step the measurements of the solids mass flows and
corresponding particle size distributions, which have been described
in Section 2.1 in detail were used to calculate the attrited ash particle
size distribution. For this purpose both, the fractional and the integral
mass balances Eqs. (29) and (30) were solved. Fig.13 shows the result
in comparison with the measured particle size distribution of the
various flows. The attrited ash particle size distribution is a very wide
distribution. It contains all particle sizes occurring in the system, from
the coarse ash particles, which end up in the bottom ash, to the veryfine particles in the micron range, which result from attrition
processes. The thus determined AAPSD is the starting point for the
population balance modeling of the CFB system.
4.2. Particle balance modeling with the AAPSD
Tofit the calculation results to measured values some adjustments
of the models had to be done. In the cyclone model the wall friction
coefficient of the brick-lined gas cyclone in the Neumnster plant was
set to 0=0.0075.
In order to consider the entrainment of large particles into the
external heat exchanger, theelutriationparameter in Eq. (5) was set to
fK=0.4.
The population balance modeling gives a dynamic description ofthe system behavior. In the present case the calculation was started
with only sand as the solid material in the system and ash with the
AAPSD was added. Fig.14 shows the developmentof themean particle
diameter in the dense bottom zone, in the external heat exchanger
(EHE) and in the cyclone overflow. We see that the bed material in the
dense bottom zone is getting coarser, while the inventory of the EHE
becomesfiner and there is practically no change in themean diameter
at the cyclone overflow. It takes of the order of 100 h to reach a steady
state.
Fig. 15 shows the pressure profile and the profile of the solids
volume concentration under conditions of steady state. The compar-
ison with the measurements shows that the calculated steady state is
in quite good agreement with the actual situation in the Neumnster
plant.
The particle balancing model allows us now to calculate solids
particle size distributions and mass flows at any point inside the
fluidized bed system. As an example Fig. 16 shows the comparison
between measured and calculated particle size distributions in the
bottom zone of the combustion chamber, in the EHE and in the
overflow of the cyclone. The matching between measurement and
calculation is excellent. Thesame is true forthe ashmassflows leaving
theplant, which arecompared in Table 3. An interesting information is
the solids mass flow into the cyclone. We see that for an input of fresh
ash of 4.8 t/h a circulating mass flow of 1343 t/h is achieved. This
enormous solids circulation rate, which corresponds to a mass flow
rate of 11.7 kg/m2/s in the upper part of the combustion chamber, is
one of the characteristic advantages of circulating fluidized bed
combustion systems, because it is responsible for the temperature
homogeneity.Another interesting feature of population balancing modeling is
that it allows to follow the fate of individual particle classes. As a result
it is possible to calculate the average residence times of different size
classes, as it is shown in Fig. 17. We see that particle sizes below 80 m
have an average residence time of a few minutes only, whereas
particles between roughly 100 and 1000 m have residence times
Fig. 16. Measured (symbols) and calculated (lines) particle size distributions in the
combustion chamber, the external heat exchanger and in the cyclone overflow for the
Neumnster plant, together with measured and calculated solids mass flows.
Table 3
Comparison of the measured and calculated ash mass flows at the Neumnster plant
Ash stream Measured Calculated
[kg/h] [kg/h]
Cyclone overflow 2259 2259Fine ash 1508 1535
Coarse ash 1390 1361
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between 2040 h. Larger particles have residence times below 5 h,
because they are accumulating in the bottom dense bed and are
withdrawnwiththe bottom ash. As a practical conclusion onecan take
from Fig. 17 that, if supporting bed material is to be fed, one shouldchoose a size fraction between 200300 m because such a material
will be kept for a maximum time in the system.
4.3. Particle balancing modeling with consideration of attrition effects
When the attrition behavior of the bed material is known, the
PAPSDof thefuel ashcan be calculated by utilizingthe simulation tool.
The calculation is carried out with consideration of the particle
attrition, while the PSD of fuel ash fed is varied until the PSDs of the
solids discharged from the plant are identical to the measured PSDs.
The ash particle size distribution in the fuel feed is the identical with
the PAPSD.
The characteristic attrition parameters used for the calculation
were distinguished by fitting the correlations discussed in Section 3.2to the attrition rate measurements, shown in Figs. 57. The derived
attrition parameters are summarized in Table 4.
The PAPSD calculated by this procedure is depicted in Fig. 18. One
can see clearly that differences between the AAPSD and the PAPSD are
only observed for particle sizes below 200 m. Larger particles have a
limited entrainment rate from the combustion chamber and therefore
do not experience the cyclone attrition, which is the governing
attrition source here. The limited attrition the large particles are
facing, in combination with their comparatively short residence time
causes no distinct change to their particle size and thus they leave the
system almost unchanged. As it should be, the AAPSD contains more
finesthan thePAPSD, since theformer distributioncontainsthe effects
of fragmentation and attrition.
Further calculations were carried out for an alternative operating
point with a recycled ash mass flow of 3360 kg/h instead of 840 kg/h.
Both conditions were simulated using either the AAPSD, not
considering the particle attrition in the plant, or the PAPSD under
consideration of the particle attrition. Fig. 19 shows the results of the
four simulation runs. First of all, it is obvious that the particle size
distributions in the cyclone overflow and in the EHE vary to a minor
extent only, although the recycle feed rate was drastically changed.
In contrast, the particle size distribution in the dense bottom zone
of the combustion chamber becomes significantly finer with the
higher recirculation rate. One can further see that the symbols,
representing the results of the calculations using the PAPSD are
concurrent with the lines, representing the results using the AAPSD.
This can be taken as a justification for simulating the plant behavior
under various operating conditions by using the AAPSD without
consideration of the ash comminution effects inside the plant.
5. Summary and conclusions
A dynamic simulation tool to model the particle population of a
circulating fluidized bed combustor with external heat exchanger and a
recycling of a fine fraction of the bottom drain material into the
combustionchamberhas been developed. It considersthefluid dynamic
processes in the combustion chamber and in the gas cyclone, as well as
the particle attrition. Tohandle multiple solidstypes simultaneouslyand
to fulfill the massbalances, some of the fluid dynamic sub-models taken
from the literature were modified. The model allows to calculate the
solids massflowsas well as the corresponding particle size distributions
at any point inside the combustion system.
Upon entering the combustion chamber the solid fuel particles are
heated and dried. The devolatilization follows and finally the char is
burning out, leaving the primary ash behind. The particle size
Fig. 17. Residence time of particles in the Neumnster plant.
Table 4
Attrition parameters of the refuse-derived fuel ash
Attrition source Kb/c/j bb/c/j
Bubble induced attrition 3.10E13 [] 54.9
Cyclone attrition8:46E2
s2
m3
! 14.5
Jet attrition2:58E2
s2
m3
! 37.7
Fig.18. Measured ash particle size distributions and the AAPSD in comparison with the
PAPSD.
Fig. 19. Calculated PSDs for the operation with different ash recycle feed rates, carried
out using the AAPSD and the PAPSD, respectively, as feed PSDs.
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distribution of the primary ash, i.e. the primary ash particle size
distribution, is then undergoing fragmentation and attrited. These
processes have been considered in the model such that the population
balances canbe calculated if the PAPSD is known. However, in the case
of a given industrial plant for RDF combustion it is very difficult to
determine the PAPSD with sufficient accuracy.
The measurements at the Neumnster plant have shown that theaverage particle residence time in the system is of the order of 13 h,
while on the other hand, coal particles burn-out times influidized bed
combustor are in the range of several minutes. Taking into account
that most of the fragmentation and attrition occurs with the fresh
particles and this also happens in a comparatively short time, ash
formation, fragmentation and attrition influences are neglected in the
calculation of the particle population balances for the fluidized bed
system. Instead a model is suggested, were the fuel enters with the
attrited ash particle size distribution (AAPSD) into the combustion
chamber. The AAPSD concept shift ash formation, fragmentation and
attrition effects out of the fluidized bed system. For a given plant the
AAPSD can be calculated from the ash flows and their particle size
distributions leaving the plant.
The model has been applied to a refuse-derived fuelfi
red plant ofStadtwerke Neumnster. The results of the measured and calculated
mass flows and particle size distributions are in good agreement. It is
shown that the AAPSD concept is sufficient to simulate the operating
behavior of the plant. The particle balancing model provides new
insides into the operating behavior. In particular the calculations of
the residence time of different particle classes in the system reveal a
very broad residence time distribution, ranging from several minutes
to a maximum of roughly 40 h. A size fraction exists between 100 and
300 m with a maximum residence time of about 40 h.
The simulation provides a means for examining possibilities to
control the particle size distribution in the combustion system. It is
shown howrecirculation of a fine ash fraction can be used to achieve a
finer bed particle size distribution in the combustion chamber.
Acknowledgments
The help of the staff of the Neumnster plant during the mea-
surement campaigns and with supplying operating data is gratefully
acknowledged. One of the authors (K. Redemann) would like to thank
Stadtwerke Neumnster GmbH for financial support.
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Glossary
: Sharpness of the separation efficiency function of the cyclone strand, m e: Mass flowof solids entrained fromthe combustion chamber, enteringthe
gas cyclone, kg/sm v: Mass flow of solids going to the inner vortex of the gas cyclone, kg/sm AA: Mass flow of attrited ash fed into the combustion chamber, kg/sm coarse: Mass flow of the coarse ash fraction of the bottom drain material, kg/sm fine: Mass flow of the fine ash fraction of the bottom drain material, kg/sm fly: Mass flow offly ash, separated in the boiler and the multi-cyclone, kg/sm Ov: Mass flow in the cyclone overflow, kg/sm sand: Mass flow of sand fed into the combustion chamber, kg/sm uf: Mass flow of ultra fine ash, separated in the flue gas cleaning plant, kg/sVe: Cyclone inlet gas volume flow, m
3/sF: Separation efficiency function of the inner vortex of the gas cyclone, L: Dynamic gas viscosity, Pa s: Exponent for the calculation of exponential decay of the solids volume
concentration in the upper dilute zone, e: Gas loading in the cyclone inlet, g: Loading limit of the gas going to the inner vortex, g: Gas density, kg/m
3
s: Solid density, kg/m3
: Attrition history parameter, a: Offset value for the separation efficiency function of the cyclone strand,
Aw: Sedimentation area of the cyclone strand, defined in [21], m2
bb/j/c: Exponent for calculation of the bubble-induced, grid jet and cycloneattrition rate (aterial property),
cv: Solid volume concentration, cv: Solids volume concentration above the transport disengaging height, cvd: Solids volume concentration at the surface of the dense bottom zone, D: Modeling parameter for the separation efficiency function of the inner
vortex of the gas cyclone, dp: Particle diameter, mdv*: Particle size with force equilibrium on the radius with the maximum
cyclone vortex velocity, mdor: Orifice diameter of the grid jets, m
fK: Elutriation correction factor, h: Height above surface of dense bottom zone, m
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hf: Total height of the upper dilute zone, mhi: Distance between the vortexfinder and the apex in the gas cyclone, mk: Exponent for the calculation of the loading limit in the gas cyclone, Kb: Parameter for the calculation of the bubble-induced attrition rate
(material property), Kg: Model parameter for the calculation of the loading limit in the gas
cyclone, Ki: Elutriation rate, kg/m
2/s
Kj/c: Parameter for the grid jet and cyclone attrition rate (material property),s2/m3
m0: Solid mass before any attrition occurred, kgmatt: Total attrited mass, kgnor: Total number of orifices of the grid jets, rb: Bubble-induced attrition rate, kg/kg/s
rc: Cyclone attrition rate, kg/kgrj: Grid jet attrition rate, kg/sT: Total separation efficiency function of the cyclone strand, T: Reduced separation efficiency function of the cyclone strand, u: Superficial gas velocity, m/sui: Maximum tangential gas velocity in the inner vortex of the gas cyclone,
m/sut: Terminal velocity, m/s
umf: Minimum fluidizing velocity, m/sut,50,e: Mean terminal velocity of the particles in the cyclone inlet, m/sut,50,v: Mean terminal velocity of the particles going to the inner vortex, m/sws,50: Terminal velocityof a particleshavinga probability of 50% to be separated
in the cyclone strand, m/s
90 K. Redemann et al. / Powder Technology 191 (2009) 7890
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