scaling parameters for pfbc cyclone separator system ... - circe

SCALING PARAMETERS FOR PFBC CYCLONE SEPARATOR
SYSTEM ANALYSIS
Antonia Gil, Luis M. Romeo and Cristóbal Cortés
CIRCE, Centro de Investigación del Rendimiento de Centrales Eléctricas
Centro Politécnico Superior. María de Luna, 3.
50015 Zaragoza (Spain)
email: antgilma@posta.unizar.es, luismi@posta.unizar.es, tdyfqdb@posta.unizar.es
ABSTRACT
Laboratory-scale cold flow models have been used extensively to study the behaviour
of many installations. In particular, fluidized bed cold flow models have allowed developing
the knowledge of fluidized bed hydrodynamics. In order for the results of the research to be
relevant to commercial power plants, cold flow models must be properly scaled.
Many efforts have been made to understand the performance of fluidized beds, but up
to now no attention has been paid in developing the knowledge of cyclone separator systems.
CIRCE has worked on the development of scaling parameters to enable laboratory-scale
equipment operating at room temperature to simulate the performance of cyclone separator
systems. This paper presents the simplified scaling parameters and experimental comparison
of a cyclone separator system and a cold flow model constructed and based on those
parameters. The cold flow model has been used to establish the validity of the scaling laws for
cyclone separator systems and permits detailed room temperature studies (determining the
filtration effects of varying operating parameters and cyclone design) to be performed in a
rapid and cost effective manner. This valuable and reliable design tool will contribute to a
more rapid and concise understanding of hot gas filtration systems based on cyclones.
The study of the behaviour of the cold flow model, including observation and
measurements of flow patters in cyclones and diplegs will allow characterising the
performance of the full-scale ash removal system, establishing safe limits of operation and
testing design improvements.
1

INTRODUCTION
Hot gas cleaning plays an essential role in the development of new power generation
technologies such as Integrated Gasification Combined Cycle (IGCC) or Fluidized Bed
Combustion (FBC). The removal of solid particles from the combustion flue gases is essential
in order to maintain gas turbine working conditions and particle emissions in safe limits. In
particular, in PFBC power stations the entrainment of bed particles may lead to erosion and
fouling in downstream equipment. Special importance is the damage of gas turbine blades. In
addition, fly ash can also produce corrosion due to metal alkali compounds.
Cyclone separator systems offer nowadays one of the best solution for removing
particles from high temperature high pressure installations. Combustion gases from
pressurized beds are an example of this harsh environment, and cyclones are, nowadays, the
only solution commercially available for these power stations. These systems are simple, low
cost and maintenance with relatively high collection efficiency. Its main disadvantages are the
complex hydraulic behaviour and a efficiency decrease for small particles (below 5 μm). In
Escatrón PFBC power plant, the hot gas filtration equipment is a two-stage process performed
in nine streams between the fluidized bed and the gas turbine. The cyclones are high
efficiency, Van Tongeren´s type, with a tangential inlet, cylindrical body, conical base, and an
axial outlet for clean gases and outlet port for solid particles in the lower part. The solid
extraction bin has been replaced by a dipleg (similar to those found in catalytic cracking) and
a suction nozzle through which collected particles are evacuated along with some amount of
transport gas. In contrast with other devices, such as series of pressure-tight lockhooppers, the
solid extraction by pneumatic conveying improves cyclone efficiency and allows reliable
handling and cooling of ash particles with low cost.
Ash and combustion gases exit the pressurized bed at nearly 800 °C and 11 bar(g). The
gas and solid mass flow rates depend on load, coal and sorbent characteristics and other
operating variables, in particular those related with fluidisation. These parameters have a
strong influence on the separation efficiency of the cyclones, and there are not well
established theories able to achieve an accurate and complete prediction. Operating
experience at Escatrón have shown sintered deposits and unsteadiness in the dipleg and the
suction nozzle that modify cyclone separation efficiency and affect the cyclone performance
and the capacity of ash conveying lines.
The possibility of achieving analyses to establish the influence of different variables in
a real installation is limited due to a non-controlled operating conditions and a lack of data to
2

obtain conclusions. Laboratory-scale cold flow models have been used extensively to study
the behaviour of many installations. In particular, fluidized bed cold flow models have
allowed developing the knowledge of fluidized bed hydrodynamics. In order for the results of
these researches to be relevant to commercial power plant, cold flow models have to be
properly scaled. In the present study, scaling parameters have been developed to build a
dipleg and cyclone cold flow model of a PFBC power plant. The cold flow model permits
detailed room temperature studies, such as determining the filtration effects of varying
operating parameters and cyclone designs.
The study of the behaviour of the cold flow model, including observation and
measurements of flow patterns in cyclone and dipleg, will allow characterising the
performance of the full-scale ash removal system, establishing safe limits of operation, testing
design improvements and determining the filtration effects of varying operating parameters.
This paper presents the most relevant scaling parameters for a cyclone separator system and
an experimental comparison of a PFBC cyclone separator system and a cold flow model
constructed based on those parameters.
CYCLONE SCALING PARAMETERS
Collection efficiency and cyclone pressure drop are the most important variables in
cyclone behaviour. Criteria for cyclone scaling parameters, based on maintain collection
efficiency, have been proposed by several researchers (Cheremisinoff and Cheremisisnoff,
1986; Dirgo and Leith, 1986; Svarovsky, 1981, 1986; Leith and Litch, 1972; Abrahanson et
al., 1978). It is generally assumed the necessity of maintain, at least, Stokes number in order
to maintain collection efficiency. Cheremisinoff and Cheremisinoff (1986) developed the
scaling parameters by analysing the forces that influence a particle within the cyclone. They
proposed to maintain Froude,
ratio between densities and lengths, equation 1.
Fr = gD v , and Reynolds numbers, Re = dvρ
s μ g , and a
2
in
⎛ ⎞
⎜
ρs
D
η = f Fr,
Re, ⎟
(1)
⎜ ⎟
⎝ ρ gd
p ⎠
For the laminar regime of flow (Re

and Stokes numbers. He has developed these parameters from the equation for accelerated,
three-dimensional particle motion with the main assumption of Stokes regime, equation 2:
Re
p
d pρ
=
μ
g
g
v
r
Other authors only mention the importance of maintaining Stokes number especially at low
solid concentrations (Dirgo and Leith, 1986), or suggest that is the Stokes number the main
variable in cyclone efficiency (Svarovsky, 1981; Leith and Licht, 1972). Finally, Chao (1982)
for a dilute flow as the freeboard of a PFBC power plant, has suggested as scaling parameters
the Stokes and Froude number and a particle Reynolds number. The last number is necessary
when the flow regime is different from Stokes regime. Although these authors have proposed
different theories for cyclone scaling, none of them has verified their proposals in a real
installation. So, as first approximation cyclone behaviour depends on the following variables,
figure 1
< 1
( , ρ , μ , d , V , D,
g,
C )
f g s g p50
in
s _ in
(2)
ρ (3)
Figure 1. Parameters affecting cyclone behaviour
Where dp50 has been selected as variable to take into account the particle size distribution at
cyclone inlet. Selecting vin, ρg and dp50 as independent variables in order to identify
dimensionless groups:
ΔP
Vin
Cs
ρs
ρg
μg
dp
η
1-η
D
g
4

⎛
⎜
gD ρ g DV
f ,
⎜ 2
⎝V
in μ g
in
2
where = V gD is the Froude number. With the approximation of a flow regime with low
Fr in
relative velocity for the particles in the cyclone and considering the influence of the
aerodynamic forces by means of the Stokes number (which is a combination of three of the
previous numbers, equation 5).
Stk
Finally, equation (4) is rearranged to read:
,
D
d
p50
ρ
,
ρ
s
g
g
C
,
ρ
s _ in
s
⎞
⎟
⎠
g
(4)
2
2
ρ g DVin
⎛d
p50
⎞ ρ ρ s sd
p50Vin
= ⎜ ⎟ =
(5)
μ
g
⎜
⎝
⎛
⎜
ρ
f Fr,
Re, St,
⎜
⎝ ρ
g
D
⎟
⎠
s s _ in C
,
Froude number takes into account the relation between gravitational and inertia forces.
When particle diameter is small, less than 10 μm, some authors neglect this number due to the
fact that gravitational forces are small compared with inertia forces (Mothes and Löffler,
1985). In our case, more than 80% of the particles are bigger than 10 μm so, it seems
necessary to maintain Froude number.
Reynolds number is not considered to analyse cyclone collection efficiency.
Generally, its influence is near negligible due to Reynolds number is high enough. According
to experiments at different temperatures and pressures, from 1 to 6 bars, and from 293 to
1123ºC, Reynolds influence is significant for values from 10 3 to 10 5 . The tendency observed
is that Reynolds higher than 10 5 does not influence cyclone behaviour (Morweiser and
Bohnet, 1996).
Most of the authors take into account Stokes number to analyse cyclone collection
efficiency. Stokes number relates the inertia forces with aerodynamic forces in a flow field.
Stokes number and cyclone efficiency are closely related. Generally, researchers consider
laminar flow or assume Stokes´ law (Rep

with Stokes number for dp50, but it does not give an exact idea of the PSD conservation. It is
possible to have a wide PSD, and a narrow PSD with the same dp50 and the cyclone behaviour
would be completely different. Finally, from a practical point of view, it is impossible to
achieve a scaled PSD. In Escatrón PFBC less than 1% of particles are smaller than 0.4 μm,
that is the limit for Rep

parameters that were used to calculate the values of the cyclone scaling parameters, and the
dimensions of the 1/5 scaled cyclone. The real cyclone mean particle diameter, dp50, has been
taken from design data, since to it is not possible to obtain a particle sample from the cyclone
inlet. Table 2 shows a comparison between the values of the dimensionless scaling parameters
for the two cyclone systems.
Table 1. Comparison between Escatrón PFBC and laboratory cold flow model parameters of
the cyclone separator system
REAL CYCLONE
SEPARATOR SYSTEM
LABORATORY COLD
FLOW MODEL SYSTEM
D (mm) 1000 200
T (K) 1030 293
P (bar a) 11.14 3.22
μg (kg/m s) 4.25e-5 1.82e-5
ρg (kg/m 3 ) 3.8 3.8
ρs (kg/m 3 ) 2800 2800
dp50 (μm) 40 23
Vin (m/s) 30 13.4
Cs_in (g/m 3 ) 290 290
Mair (kg/s) 10.6 0.19
Mash (g/s) 800 14
Table 2. Comparison of Escatrón PFBC and cold flow dimensionless scaling parameters
Froude number
Reynolds number
Stokes number
Density ratio
REAL CYCLONE
SEPARATOR SYSTEM
LABORATORY COLD
FLOW SYSTEM
2
Fr = vin
gD
91.74 91.79
ρ g Dvin
Re = 2.68 e+6 5.60 e+5
μ
Stk =
d
ρs p
2
50
Solid
concentration ρ s
g
v
in
g
Dμ
g
3.16 5.45
ρ s
736.8 736.8
Cs
_ in
ρ
104 e-6 104 e-6
7

DIPLEG SCALING PARAMETERS
The collected particles removed from the PFBC cyclone system flow down a dipleg
and are transported by means of pneumatic conveying thought a suction nozzle in the bottom
of the dipleg. There are no specific models of this flow inside the dipleg, so an approximate
analysis, resorting to reasonable and simple models of the physical situation, is appropriate.
Flow patterns inside the dipleg may be expected to possess the following features:
— Particles slid down on the dipleg wall, following a helical path of variable pitch.
— The gas flow generally follows two paths: near the wall, it moves downwards, with
tangential and axial velocity components, whereas it is reversed at the leg core,
forming an upward flow.
As first approximation dipleg behaviour depends on the following variables
( , ρ , , D , L,
V , V , g,
C )
f ρ μ
(7)
g
s
g
In this case, selecting, L, ρg and Vax as independent variables in order to identify
dimensionless groups and rewriting
dl
ax
t
⎛
2 ⎞
⎜
D
ρ
dl ρs Vax
V L gV
ax ax
f , , C
⎟
⎜
sol , , ,
(8)
⎟
⎝ L ρ g Vt
gL μ
⎠
A 1/5 scaled model has been built for the dipleg. This factor has been chosen to simulate the
whole PFBC cyclone system. First dimensionless group is a ratio between dipleg dimensions
and it is maintained. Particle-solid densities ratio is also conserved since it was also a
dimensionless group in cyclone scaling. Solid concentration as solid- air flow through dipleg
is maintained with the assumption of cyclone efficiency is similar. Velocities ratio
dimensionless number is equal to the tangent of the sliding particle velocity. Particles
tangential velocity is supposed to be proportional to the tangential velocity calculated with
Alexander equation (Alexander, 1949):
sol
V r cte
n
t = (9a)
( ) ⎟ ⎟
0.
3
⎛ ⎞ ⎞
0.
14 T
1−
0.
67D
* ⎜ ⎟
⎛
n = 1−
⎜
⎜
dl
(9b)
⎝
⎝283⎠
⎠
Particle axial velocity is proportional to the gas velocity though the dipleg and could be
estimated as
V
m
= (10)
a _ nozzle
ax ρ g Asn
8

The conservation of the transport air flow makes the sliding angle to be conserved. This takes
into account the effects of vortex extending due to suction. This effect could modify the
dipleg flow patterns, so it is important to maintain it constant:
V
V
ax
t
msn
=
ρ A
g
sn
1 ⎛ Ddl
⎜
V ⎝ D
in
⎞
n
⎟
⎠
m
=
m
sn
air
A
A
in
sn
⎛ D
⎜
⎝ D
The small difference in the values of exponent n in Alexander equation modifies slightly the
sliding angle between PFBC cyclone and cold flow model. This difference could be estimated
as a 1.6 % and can not be reduced since n depends on the temperature. Froude number is
calculated as a relation between axial velocity, dipleg length and gravity. Because of the
conservation of transport air, Froude number is maintained. Finally, Reynolds number could
not be conserved due to gas viscosity is fixed by the cold flow model temperature.
Table 3 lists the dipleg geometric and operating variables. They have been used to
calculate the dipleg scaling parameters and dipleg erection. Table 4 summarised the
dimensionless parameters of the dipleg, the values of the scaling parameters were closely
matched between the cold flow model and the Escatrón PFBC except for Reynolds number.
Table 3. Comparison between Escatrón PFBC and laboratory dipleg cold flow model
parameters
dl
n
⎞
⎟
⎠
REAL DIPLEG LABORATORY COLD
FLOW MODEL DIPLEG
Ddl (mm) 400 80
L (m) 9.15 1.83
T (K) 1030 293
P (bar a) 11.14 3.22
ρg (kg/m 3 ) 3.8 3.8
ρs (kg/m 3 ) 2800 2800
Mair (kg/s) 10.6 0.19
Mnozzle (g/s) 163 2.9
Mash (g/s) 800 14.0
(11)
9

Table 4. Comparison of dipleg Escatrón PFBC and cold flow model dimensionless scaling
Dipleg dimensions
Density ratio
Solid concentration
Velocities ratio
Froude number
Reynolds number
parameters
ESCATRON PFBC
REAL DIPLEG
LABORATORY COLD
FLOW MODEL DIPLEG
L
Ddl
22.0 22.0
ρ s
ρ
736.8 736.8
g
C =
M
75 e-3 74 e-3
sol
ash
M air
Vax 0.568 0.559
V
t
2
ax
Fr = V gL
105.3 105.4
Lρ
gVax Re =
μ
CYCLONE AND DIPLEG COLD FLOW MODEL
1.96 e+5 4.08 e+4
Figure 1 shows cyclone and dipleg built with the similarity criteria aforementioned
and have linear dimensions which are one-fifth those of the real PFBC dimensions. Figure 2
shows the cold flow model device that is made up of the following components:
- Two air-pressure supplies: main (L1) and a secondary line (L10) for
fluidisation of the particle-discharging hopper.
- Pressurized solid storage tank (T1) and variable speed rotary valve connected
to a Venturi nozzle (L3).
- Primary cyclone inlet (L4), air with a design solid concentration of 290 g/m 3 .
- Experimental primary cyclone (T2), equipped with a PMMA dipleg (T4).
- Secondary cyclone (T3) with a solids-collecting bin (T7).
- Two sedimentation chambers with fabric filters for complete collection of
particles and cleaning of the exhaust air (T5 and T6).
- Control of airflow by flow meters and valves downstream the sedimentation
chambers (I1 and I2)
10

control
pressure valve
hopper
fluidisation
T P
Pin= 2.21 bar(g)
Tin= 20 °C
ash flow= 50 kg/h
air flow= 680 kg/h
a
Figure 1. Scaled cyclone dimensions
b
De
D
B
S
h
H
L
Dimensions
a/D 0.460
b/D 0.203
De/D 0.307
S/D 0.891
h/D 1.310
H/D 3.795
B/D 0.399
L/D 9.022
Figure 2. Laboratory cold flow model cyclone separator system
ash
hopper
rotary feeder
P ΔP
primary
cyclone
ΔP
ash extraction
dipleg
suction
nozzle
.
secondary
cyclone
T P F
filter 1
T P F
filter 2
clean air
clean air
11

CYCLONE AND DIPLEG EXPERIMENTAL COMPARISON
Experimental scaling verification is based on a comparison of pressure drop. Cyclone
pressure drop has a strong influence on collection efficiency. The impossibility to take data of
collection efficiency at PFBC power station to compare with cold flow model has made us to
validate the scaling parameters based on cyclone pressure drop. For pneumatic transport as in
dipleg, pressure drop plays an essential role in its analysis. Probes have been placed in several
points though dipleg, and partial and total dipleg pressure drop have been obtained for
verification.
The data used in the following scaling comparisons were taken at operating conditions
after a periodic overhaul of the Escatrón PFBC, with cyclones revised and cleaned of sintered
deposits. The data used in the scaling comparison were taken at a single operating condition
and in steady- state operation. The PFBC power plant load was approximately 90% of the full
load with a standard deviation of 1 MW. Cold flow model pressure drop data were taken
using pressure transducers with a range of 0/62 mbar for cyclone pressure drop and –62/+62, -
37/+37, -37/+37 and –5/5 mbar for dipleg. The data from Escatrón PFBC were obtained with
pressure transducer with a range of 0/490 mbar for cyclone pressure drop, ad –98/+98 mbar
for dipleg pressure drop. Data uncertainty is about 0.4% of span.
PFBC cyclone pressure drop transducers are installed in five of the nine cyclones.
Data from pressure drop varies from a maximum of 199.2 mbar to a minimum of 141.0 mbar.
Table 5 shows the PFBC data and its comparison with cold flow model data.
PFBC pressure drop data shows discrepancies between real cyclones. Most probably, a
combination of ashes and gases non-homogeneity at cyclone inlet could cause these
discrepancies. Another cause to explain this effect is cyclone fouling. As it will be proved in a
next paper (Romeo et al., 1999), fouling causes a reduction in cyclone pressure drop. A
different fouling between cyclones could be the cause of discrepancies in real data.
In order to compare and validate the cold flow model, it is necessary to scale down the
Escatrón PFBC cyclone pressure drop data or scale up the cold flow model data. The
dimensionless variable for the pressure drop is
⎛ C ⎞
Δ P ⎜
ρs
s _in
=
⎟
2 f Fr , ,
(12)
1 ρV
⎜ ⎟
2 in ⎝
ρ g ρs
⎠
The right-hand term of the equation (12) is conserved due to the maintenance of
dimensionless numbers that affect cyclone behaviour. So, to scale pressure drop data it is
12

necessary take in account the velocity ratio to the power of two, it means to operate by a
factor of five.
The agreement between Escatrón PFBC pressure drop data and cold flow model data
scaled up is excellent, as indicated in table 5. For the PFBC cyclones, the pressure drop has an
average of 168.0 mbar and a standard deviation of 20.3 mbar, the 99% of the data would be in
the range of 127.4/208.6 mbar. In the cold flow model, the average is 148.5 mbar with a
standard deviation of 9.0 mbar, so the 99% of the data would be in the range of 124.0/166.5
mbar. The latter range of data is approximately inside the former one. This agreement
provides a verification of the scaling proposed above.
Table 5. Comparison between PFBC and cold flow model cyclone pressure drop data
Cyclone 1
Cyclone 3
Cyclone 5
Cyclone 7
Cyclone 9
Average of five PFBC
Cyclones
Cold flow Model
Cyclone
Cold flow Model
Cyclone Scaled data
Maximum Minimum Average
191.4
199.2
174.9
150.8
145.4
175.7
190.3
167.7
142.9
141.0
182.5
194.7
172.3
147.7
143.1
Standard
deviation
7.00
3.83
2.95
2.89
1.72
194.7 143.1 168.0 20.5
34.43 24.06 29.73 1.79
172.2 120.3 148.5 9.0
Tables 6 and 7 show also a comparison between PFBC and cold flow model dipleg
pressure drop data. Three zones are observed in the dipleg, an upper one where the pressure
drops strongly. An intermediate region where the pressure drop is negative and particles are
going down vertically. Finally, the last zone near the suction nozzle where the pressure drops
due to pneumatic transport. These three zones are observed both, in the PFBC and the cold
flow model, so that qualitatively the behaviour or the diplegs are similar, although a
difference in values is also observed. Table 6 shows the data at real and cold flow model
dipleg.
13

Table 6. Comparison between PFBC and cold flow model dipleg pressure drop data
PFBC dipleg pressure drop 1
PFBC dipleg pressure drop 2
PFBC dipleg pressure drop 3
Cold flow model dipleg pressure drop 1
Cold flow model dipleg pressure drop 2
Cold flow model dipleg pressure drop 3
Maximum Minimum Average
63.2
- 3.44
22.3
60.6
- 4.94
16.3
61.8
- 3.94
18.1
2.50
- 0.18
Standard
deviation
In table 7 the scaled data for the cold flow model is compared with real data. Scaling
up has been done in the same manner as cyclone scaling up, i.e. the velocity ratio to the power
of two. In spite of the similar tendencies in pressure drop, the scaling is not as good as the
cyclone scaling. In this case the effect of varying Reynolds number is affecting the agreement.
Taking into account the Reynolds influence and multiplying by 5 (PFBC and cold flow model
Reynolds relation) the agreement of pressure drop in the two upper zones is excellent.
Possibly, a combination of suction and ash deposition is the responsible of discrepancies in
the lower zone pressure drop data. In addition, the effect of fluidisation air in PFBC dipleg
bottom has not been taken into account in the cold flow model constructed, and it could
modify the measurements or the behaviour in this zone. Further studies are necessary to
explain this discrepancy.
Table 7. Comparison between PFBC and cold flow model dipleg pressure drop data
Pressure drop 1
Pressure drop 2
Pressure drop 3
PFBC data Cold flow model
61.8
- 3.94
18.1
data
2.50
- 0.18
0.04
Scaled data
12.5
- 0.9
0.2
0.04
1.02
0.54
2.31
Scaled data and
Reynolds
influence
62.5
- 4.5
1.0
14

CONCLUSIONS
A 1/5-scale model of the Escatrón PFBC cyclone system has been constructed based
on scaling parameters. Comparisons of cyclone pressure drop from the cold flow model and
Escatrón PFBC indicates that the cyclone behaviour of the two cyclones is similar. Because of
cyclone pressure drop is one of the most important parameters in collection efficiency, it is
assumed the cyclone efficiency would be maintained in both systems. This point remains
open due to the impossibility to validate the cold flow model results at the real system.
An analysis of the main variables in PFBC cyclone dipleg has been done. This study
has not been addressed before. It has been impossible to maintain all the scaling parameters
that influence dipleg behaviour. Reynolds number has not been maintained due to cyclone
scaling determinate the value of some variables in dipleg behaviour. Reynolds influence has
been taken into account to validate the cold flow model data. Comparison of dipleg pressure
drop from the cold flow model and Escatrón PFBC show a good agreement through the
dipleg. In the suction nozzle some discrepancies has been observed. The reason for these
discrepancies could be the different behaviour of the ash conveying lines in Escatrón PFBC
and the sedimentation chamber in the cold flow model. Further studies are needed to fully
understand fluid flow around suction nozzle.
The cold flow model is revealed as an important tool to optimize and understand the
cyclone system behaviour. It is also useful to know the influence of different operational
variables. At present, these studies are being carried out.
ACKNOWLEDGEMENTS
This research has been fully supported by ENDESA, S.A. Mr Alfonso Ruiz, director
of Escatrón PFBC power station, Dr. Emilio Menéndez, head of the R&D department of
ENDESA, S.A., and Mr. Diego Martínez, head of the R&D department at Escatrón are
gratefully acknowledged for making possible the project and for all the facilities provided.
Escatrón power plant personnel are also acknowledged for their useful assistance.
NOMENCLATURE
Asn
Cs_in
Csol
suction nozzle area (m 2 )
solid concentration at cyclone inlet (g/m 3 )
solid concentration at dipleg (g/m 3 )
D cyclone diameter (m)
15

Ddl
dp
dp50
dipleg diameter (m)
particle diameter (m)
particle diameter at 50% of the PSD (m)
Fr Froude number
g gravity acceleration (m/s 2 )
L dipleg length (m)
ma_nozzle
Mair
Mash
P pressure (bar)
air flow through the suction nozzle (g/s)
air flow at cyclone inlet (kg/s)
ash flow at cyclone inlet (kg/s)
Re Reynolds number
Rep
particle Reynolds number
Stk Stokes number
T temperature (K)
Vax
Vin
vr
Vt
Greek Leters
axial velocity at dipleg (m/s)
inlet cyclone velocity (m/s)
relative velocity (m/s)
tangential velocity at dipleg (m/s)
η cyclone efficiency (%)
ρg
μg
ρs
REFERENCES
gas density (kg/m 3 )
gas viscosity (kg/m s)
solid density (kg/m 3 )
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Chao BT (1982) Scaling and Modelling. Handbook of Multiphase Systems. Edited by
Gad Hetsroni, Hemisphere Publishing Co, pp.(3)44-(3)48
16

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