article-cyclone.pdf

Chemical Engineering and Processing 43 (2004) 511–522
Comparison of different models of cyclone prediction performance for
various operating conditions using a general software
S. Altmeyer∗, V. Mathieu, S. Jullemier, P. Contal, N. Midoux, S. Rode, J.-P. Leclerc
Laboratoire des Sciences du Génie Chimique de Nancy, CNRS-ENSIC, 1, rue Grandville, BP 451, 54001 Nancy Cedex, France
Received 14 August 2002; received in revised form 25 March 2003; accepted 28 March 2003
Abstract
A new software is presented which allows to calculate cyclone efficiency for a given geometry or to determine a geometry for a desired
efficiency is presented. It has been established for cyclones with relatively low solids loading (<10 g/m3
) and it applies for pressure drop
between 10 and 10 000 Pa, for cut diameter between 0.2 and 20 ␮m, for volumetric flow rate from 10−4
to 1000 m3
/s and for cyclone diameter
from 0.01 to 3 m. The calculations are realised with four models presented in the literature. Comparison between model predictions and
published measurements, shows that models used in the software predict pretty well the experimental results, obtained in a large range of
operating conditions. Moreover, a comparison of the results obtained with these four models permits to select the model the most adapted,
depending on inlet flow rate, temperature and pressure used.
© 2003 Elsevier B.V. All rights reserved.
Keywords: Cyclone prediction; Cyclone efficiency; General software; Gas-solid separators; Cyclone design
1. Introduction
Cyclones are mostly used for removing industrial dust
from air or process gases. They are the most frequently en-
countered type of gas–solid separator in industry. The pri-
mary advantages of cyclones are economy, simplicity in
construction and ability to operate at high temperatures and
pressures.
The principle of cyclone separation is simple: the
gas–solid mixture enters on the top section. Then, the cylin-
drical body induces a spinning, vertical flow pattern to the
gas–dust mixture. Centrifugal force separates the dust from
gas stream: the dust travels to the walls of the cylinder and
down the conical section to the dust outlet and the gas exits
through the vortex finder.
The choice of cyclone geometry is difficult and often em-
pirical. In order to assist this choice, a software cyclone
was created which permits to calculate efficiency of cyclone
for a known geometry or to determine a geometry for a de-
sired efficiency.
∗ Corresponding author.
E-mail address: progepi@ensic.inpl-nancy.fr (S. Altmeyer).
Four models were chosen to realise the calculations. The
results of the four calculation models are compared with
experimental data found in the literature for different inlet
flow rates, pressures and temperatures. In the literature, there
are only a few reports comparing different models [1,2],
the software presented here allows to compare easily the
different models and to propose the most adapted one for
different possible operating conditions.
Numerical calculations are more and more used to sim-
ulate the flow field in a cyclone [3,4]. However, up to now
computational fluid dynamics (CFD) simulations do not al-
low to evaluate correctly the efficiency. Semi-empiric models
remains are, therefore, still very useful to design cyclones.
2. Design of a cyclone
2.1. Selected cyclone design
Cyclone exists under different forms but the reverse flow
cyclone represented in Fig. 1 is the most common design
used industrially. The cyclone consists of four main parts:
the inlet, the separation chamber, the dust chamber and the
vortex finder.
Two types of inlet are available: the axial and the tangen-
tial inlets shown in Fig. 2. When using an axial inlet, the ro-
0255-2701/$ – see front matter © 2003 Elsevier B.V. All rights reserved.
doi:10.1016/S0255-2701(03)00079-5

512 S. Altmeyer et al. / Chemical Engineering and Processing 43 (2004) 511–522
Fig. 1. Cyclone design configuration.
Fig. 2. Type of inlet constructions.
tating flow is generated by guide blades, which distribute the
gas flow over the whole circumference of the cyclone. This
construction is widely used for the separation of droplets
from gases. Tangential inlets are preferred for the separation
of solid particles from gases. For the moment, the software
deals with the most standard case of reverse flow cyclone
with a tangential rectangular inlet.
2.2. Description of the chosen models
Since the first application of aerocyclones in 1886, sev-
eral models have been developed for the calculation of the
design parameters, pressure drop and efficiency. All these
approaches can be divided into six groups:
• Mathematical and numerical models.
• Diffusion models.
• Characteristic number models.
• Residence time models.
• Force balance models.
• Models, which combine aspects of the force balance and
the résidence time model.
Bohnet et al. [1] realised an analysis which showed that
force balance models and combined models are best suited
for the calculation of aerocyclone. Due to the physically
simplified assumptions (characteristic number and residence
time) and the high calculation expenditure (numerical and
diffusion models), the use of the first four models is rather
limited.
We have thus chosen four models based on the best suited
models:
• Barth [1].
• Leith and Licht [2,5,6].
• Mothes and Löffler [7].
• Lorenz [8].
The first two models are based on force balance and the
following two on a combination of force balance and resi-
dence analysis. The following part presents some of the ele-
ments used to conceive these models. The aim is to present
the assumptions made and the principle of calculation of the
models.
2.2.1. First considerations
Some assumptions are common to all these models and
can be consider reasonable enough to obtain a good com-
promise between accurate prediction and simplification of
the equations. They are:
• The particles are spherical.
• The particle motion is not influenced by the presence of
neighbouring particles.
• The radial velocity of the gas equals zero.
• The radial force on the particle is given by Stokes’s law.
2.2.2. Barth model
Barth (cited in [1]) proposed a simple model based on
a force balance. This model enables to obtain the cut-size
and the pressure drop values. The principle of calculation
consists on the fact that a particle carried by the vortex
endures the influence of two forces: a centrifugal force Z
and a flow resistance W. They are expressed at the outlet
radius Ri where the highest tangential velocity occurs:
W = cw
π
4
d2
pc
ρ
2
w2
r (1)
Z =
π
6
d3
pc(ρp − ρ)
u2
r
(2)
Cw =
24
Rep
=
24µ
dpcwr(Ri)ρ
(3)
The tangential velocity at Ri equals:
wr(Ri) =
V0
2πRi(H − L)
(4)
The radial velocity u(Ri) equals:
u(Ri) =
V0
πR2
i
Se
S
α
Rα
Ri
+ λ
heq
Ri
(5)
where:
heq =
Stot
2π

Rc
Ri
(5.1)

S. Altmeyer et al. / Chemical Engineering and Processing 43 (2004) 511–522 513
Table 1
Geometry used to test the model of Barth
Dc (m) Di/Dc a/Dc b/Dc h/Dc L/Dc H/Dc Ds/Dc
0.15 0.33 0.53 0.13 0.69 0.73 2.58 0.33
α = 1 −

0.54 −
0.153
Se
S

b
Rc
1/3
(5.2)
λ = 0.05 +
287.4
Rew
(5.3)
Rew =
Dc . ρ
µ
.
V0
ab

0.089 − 0.204
b
Rc
(5.4)
␣ is a correction factor for contraction, expressed as a func-
tion of the inlet geometry (the equation presented shows the
case of a rectangular tangential inlet) and λ a friction factor
either equals to 0.02 or a function of the inlet geometry and
the inlet flow rate described by Muschelknautz and Brunner
[18].
The pressure drop is resolved into two terms. The first
term ζi reflects the contribution by inlet losses and fric-
tion losses. The second term ζe results from the flow losses
through the outlet pipe.
P = (ζe + ζi)
ρ
2
w2
(Ri) (6)
with:
ζe =
Ri
Rc



1
1 −
u(Ri)heq
w(Ri)Ri
λ
2
− 1




u(Ri)
w(Ri)
2
(6.1)
ζi = f

2 + 3

u(Ri)
w(Ri)
4/3
+

u(Ri)
w(Ri)
2

(6.2)
This model is relatively simple but it allows to obtain eas-
ily an approximation of the pressure drop and the cut di-
ameter which are the two main parameters for an industrial
approach.
The validity of this model was confirmed by comparing
its predictions with experimental values obtained under the
experimental conditions presented in Tables 1 and 2 [1].
2.2.3. Leith and Licht model
This model [2,5,6] takes into account the temperature and
provides the cut-diameter, the pressure drop and the effi-
ciency of separation for a particle of diameter dp.
Table 2
Experimental conditions used to test the model of Barth (charge load not
specified)
Vinf (m3/s) Vsup (m3/s) T (K) P
0 0.033 293 Atm
Leith and Licht describe particle motion in the entry and
collection regions with the additional following assump-
tions:
• The tangential velocity of a particle is equal to the tan-
gential velocity of the gas flow, that is, there is no slip in
the tangential direction between the particle and the gas.
• The tangential velocity is related to the radius by:
uRn=constant.
A force balance and an equation on the particles collection
yields Eq. (7):
η = 1 − exp

−2

GτV0
D3
c
(n + 1)
0.5/n+1

(7)
where:
G =
4Dc(2Vs + V)
a2b2
(7.1)
n = 1 −

1 −
(12Dc)0.14
2.5

T + 460
530
0.3
(7.2)
τ =
ρpd2
p
18µ
(7.3)
Note: G is a factor related to the configuration of the cyclone,
n is related to the vortex and τ is the relaxation term.
The pressure drop is described by Eq. (8):
P = 0.003ρ

16V2
0
abD2
i

(8)
The cut-size is given by Eq. (9):
dpc =

9µDcab
4πNtV0(ρp − ρ)
(9)
where
Nt =
V0
ab
×

0.1079−0.00077
V0
ab
+ 1.924×10−6
×

V0
ab
2

(9.1)
Nt is the number of times the gas turned around in the cy-
clone between its inlet and its outlet and is a function of the
flow rate and the inlet geometry.
This model is easy to handle. Moreover, it takes temper-
ature into account via its influence on efficiency but it is
based on simplified physicals assumption. Lorenz [8] shows
that the efficiency for the small particles calculated with this
model is higher than that calculated with the others models.
The validity of this model was confirmed by comparing
its predictions with experimental values obtained under the
experimental conditions presented in Tables 3 and 4 [2,6].

Table 3
Geometry used to test the model of Leith and Licht
Geometry 1 0.2032 0.5 0.5 0.2 1.5 0.5 4 0.375
Geometry 2 0.3048 0.5 0.583 0.208 1.33 0.583 3.166 0.5
Geometry 3 0.2794 0.527 0.841 0.264 1.527 1.055 2.873 0.527
Geometry 4 0.4699 0.527 0.838 0.254 1.524 1.054 2.865 0.527
Table 4
Experimental conditions used to test the model of Leith and Licht (charge
load not specified)
Vinf (m3/s) Vsup (m3/s) Tinf (K) Tsup (K) P
0.06 0.13 310 422 atm
2.2.4. Lorenz model
This model [8] based on the four assumptions below, takes
into account the temperature and provides the cut-diameter,
the pressure drop and the efficiency of separation for a par-
ticle of diameter dp.
2.2.4.1. Hypotheses.
• The tangential velocity depends only on the coordinate R
and not on the axial coordinate (z).
• The particle motion is determined as the sum of a random
movement (due to the gas) and a collective movement
(due to the flow of particles).
• For the removal of particles from the gas, the particles
must be prevented from entering the upward flow into the
exit and must deposit on the wall of the cyclone during
their residence time.
• Re-entrainment of already deposited particles from the
conic part is essentially due to the increasing turbulent
back-mixing of particles on the cyclone bottom.
The model is based on calculations made on the cyclone
subdivided into five parts as presented in Fig. 3.
The principle of the model is to form a differential system
with mass balances in each region. The equations of the
system depend on the geometry, the inlet flow rate and the
two following main parameters:
• ji(z): particle flux at the height z and in the region i.
• ci(z): concentration of particles at the height z and in the
region i.
2.2.4.2. Parameters used in the system.
Equivalent cyclone. For the commodity of the calcula-
tion, Lorenz defines an equivalent cyclone of same height H
and of radius R∗
c.
R∗
c =

Vcyclone
πH
(10)
Fig. 3. Cyclone geometry used in calculations of Lorenz.
The secondary flow. The secondary flow is in the bound-
ary layer along the cover plate and the outside of the vortex.
This flow has to be considered because the boundary layer
carries particles, which can reach the cyclone outlet without
entering into the separation zone. Lorenz calculates it using
equations from Ebert (cited in [8]) where n is the vortex ex-
ponent, δd the absolute boundary layer thickness and Φ is a
shape factor for the flow profile of the boundary layer.
Vs = 2πRcu(Rc)

R∗
i
Rc
1−n
δ(R∗
i )(0.26 − 0.154Φ) (11)
with:
δd = f(R/Rc, Re) (11.1)
n =
ln(u(R)/u(Rc))
ln(Rc/Ri)
(11.2)
Φ = −0.1 (11.3)
R∗
i = Ri + 0.053Rc (11.4)
R∗
i is the equivalent radius of the engagement length of cy-
clone. It is the sum of the real radius Ri and the thickness
of the boundary layer of the tube.

The tangential velocity. The tangential velocity at R is
calculated using the equations derived by Meissner (cited in
[10])
u(R) =
u(Rc)
R
Rc
1 + ϑ 1 − R
Rc
(12)
with
ϑ =
u(Rc)
w(Rc)

λcyl +
λcone
sin ε

In this equation θ is the angular momentum that characterises
the angular momentum exchange between the wall and the
gas. θ is a function of the velocities u(Rc), w(Rc) and of
λi: friction coefficients (λcyl, λcone). All the values λi are
considered constant. Usually this coefficient was considered
equal to 0.007. Lorenz improved the previous models by
using the following formula:
λ = λ0(1 + 2
√
ϕe) (12a)
where:
λ0 = 0.005 +
287.4
Rew
(12.1)
Rew =
u(Rc)Dcρ
µ
(12.2)
u
(Rc) =
V0
ab 0.889 − 0.204 b
Rc
(12.3)
ϕe : inlet charge (kg/kg)
Diffusivity due to turbulence. In the case of radial
exchange of particles, the model needs to take into ac-
count the diffusivity by the coefficient: Dturb given by
Eq. (13):
Dturb = 0.006

1 + arctan

Retr
136 864

(13)
Settling velocity.
ws(R) =
(ρp − ρ)d2
pu2(R)
18µR
(14)
Radial velocities.
w(Rc) = 0 (15)
w(Ri) =
(V − Vs)
2πRi(H − L)
(16)
Re-entrainment of particles. The re-entrainment of par-
ticles already separated in the lower part is taken into ac-
count. The highest possible re-entrained mass flow is defined
by the equation below:
mw = mw,max · w(Res) (17)
with:
mw,max = V0c0 − V(L)c4(L) − Vsctr(L) (17.1)
w(Res) = 0.375 − 0.238 arctan

Res − 35 776
10 548

(17.2)
Flow rate at z.



V(z) = 0 for : 0 ≤ z ≤ L
V(z) = (V0 − Vs)
(H − z)
(H − L)
for : L ≤ z ≤ H
(18)
2.2.4.3. Equations of the differential system. The system
of differential equations is obtained by writing mass balances
in each region, by calculating the particle concentration on
the axial co-ordinate z. The system is solved using boundary
conditions.
2.2.4.4. Determination of the parameters.
2.2.4.4.1. Efficiency.
η = 1 −
Vs
V0
ctr(L) +
V0 − Vs
V0
c4(L)
c0
(19)
2.2.4.4.2. Pressure drop.
P = ξ
ρ
2
w2
(Rc) (20)
with:
ξ = ξe + ξstat + ξdyn + ξi (20.1)
ξe =

u(Rc)
w(Rc)
2
−

u(Rc)
w(Rc)
2
(20.2)
ξstat =

u(Rc)
w(Rc)
2
2
(1 + ϑ)4
×

1
2R4U2
+
3ϑ
R2U
− 3ϑ ln(R2
U) − ϑ3
R2
U − 3ϑ
−0.5 + ϑ3

(20.3)
ξdyn =

u(Rc)
w(Rc)
2
(1 − U2
) (20.4)
ξi = 0.74

2 + 3

u(Ri)
w(Ri)
4/3
+

u(Ri)
w(Ri)
2

Rc
Ri
4
(20.5)
U and R are dimensionless terms:
U =
u(Ri)
u(Rc)
, R =
Ri
Rc
(21)
This model yields a complex calculation procedure. It
takes the temperature, via its influence on the diffusion coef-
ficient and on the friction factor, the re-entrainment and the

Table 5
Geometry used to test the model of Lorenz
Dc (mm) Di/Dc a/Dc b/Dc Ds/Dc H/Dc h/Dc L/Dc
Geometry 1 150 0.33 0.53 0.13 0.33 2.58 0.69 0.73
Geometry 2 150 0.23 0.53 0.13 0.33 2.58 0.69 0.73
Geometry 3 150 0.23 0.40 0.10 0.33 2.58 0.69 0.73
Table 6
Experimental conditions used to test the model of Lorenz (charge load
not specified)
Vinf (m3/s) Vsup (m3/s) Tinf (K) Tsup (K) P
0 0.056 293 1123 atm
secondary flux into account. The results obtained are satis-
factory. However, in the work of Lorenz, this model is es-
tablished and tested with three geometries only (cf. Table 5)
and the parameter are fitted to the experimental results. Not
surprisingly, the model is very adequate for these three ge-
ometries but it must be verified for the others.
The prediction of this model were compared with results
obtained at the experimental conditions presented in Tables 5
and 6 [1,8].
2.2.5. Mothes and Löffler model
As the model of Lorenz, this model yields the cut-diameter,
the pressure drop and the efficiency of separation for a par-
ticle of diameter dp. Mothes and Löffler [7] established a
model on the principle described previously in the model
of Lorenz. They were the first to propose a model based
on a differential system of equations by separating the cy-
clone into four parts. The following assumptions were made
which simplify the system:
• λ and Dturb are supposed constant
– λ = 0.007
– Dturb = 0.0125
• There is no re-entrainment
– mw = 0
• Mothes and Löffler consider that there is no separation
in the region 1 above a/2, which implies that there is no
regions d, e and tr.
– No secondary flow (Vs = 0).
At room temperature, the results obtained with this model
are satisfactory. But it becomes less satisfactory at high tem-
perature [8]. For example the error corresponding to the
pressure drop could reach more than 50% at temperature
between 700 and 850 ◦C.
Table 7
Geometry used to test the model of Mothes and Löffler
Superior values 0.095 0.779 1.05 0.316 7.579 7.579 0.307 0.779
Inferior values 0.421 0.158 2.41 2.41 3.231 0.421
Table 8
Experimental conditions used to test the model of Mothes and Löffler
(charge load not specified)
Vinf (m3/s) Vsup(m3/s) Tinf (K) Tsup (K) P
0.06 0.13 310 422 atm
The reasons, which can explain the difference between the
experimental, and the theoretical results are the following:
• The friction coefficient λ is taken constant, therefore, it
is implicitly assumed that the viscosity has no influence
on the friction.
• Re-entrainment of particles is not taken into account in
the calculation
• The coefficient of diffusivity is taken constant. Therefore,
it is not dependent on the flow.
• The coefficient of pressure drop is only dependent on the
geometry and not on the volumetric flow rate, the viscosity
or the density.
This model was compared with data obtained at the ex-
perimental conditions presented in Tables 7 and 8 [7].
2.3. Software used for the calculation
The software cyclone (cf. Fig. 4) enables to calculate
efficiency of a cyclone for a known geometry or to give a
geometry for a desired efficiency.
The four models described previously are available in the
software. The knowledge of some parameters is necessary
to make the calculation:
• gas characteristics (temperature, pressure, viscosity and
density)
• solid characteristics (solid distribution and density)
The software gives the choice between defined configura-
tions of the cyclone used by the conceivers of models. These
classical geometries are reported in the Table 9. The inter-
esting point is that, once the configuration is chosen, there
is just one parameter (cyclone diameter) to evaluate to ob-
tain all cyclone dimensions. It is also possible to use its own
geometry.

Fig. 4. Graphic interface of the software ‘cyclone’.
Table 9
Geometric ratios for eight models
a/Dc b/Dc Ds/Dc Di/Dc H/Dc L/Dc h/Dc
LAPPLE 0.5 0.25 0.25 0.5 4 0.625 2
SWIFT1 0.5 0.25 0.4 0.5 3.75 0.6 1.75
SWIFT2 0.44 0.21 0.4 0.4 3.9 0.5 1.4
STAIRMAND 0.5 0.2 0.375 0.5 4 0.5 1.5
PETERSON and WHITBY 0.583 0.208 0.5 0.5 3.173 0.583 1.333
LORENZ1 0.533 0.133 0.333 0.333 2.58 0.733 0.693
LORENZ2 0.533 0.133 0.333 0.233 2.58 0.733 0.693
LORENZ3 0.4 0.1 0.333 0.233 2.58 0.733 0.693
Five parameters are calculated by the software:
• volumetric flow rate,
• cyclone diameter,
• cut diameter,
• cyclone efficiency,
• pressure drop.
To run the software, the user needs to enter two parame-
ters, the other parameters are calculated. The combinations
available are:
• volumetric flow rate and cyclone diameter,
• cyclone efficiency and cyclone diameter,
• cut diameter and cyclone diameter,
• pressure drop and cyclone diameter,
• cyclone efficiency and volumetric flow rate,
• cut diameter and volumetric flow rate,
• pressure drop and volumetric flow rate.
For the following combinations, the user needs to indicate in
addition the order of magnitude of the volumetric flow rate.
• pressure drop and cyclone efficiency,
• pressure drop and cut diameter.
The following part compares the results obtained by the
four models depending on inlet flow rate, temperature and
pressure used.
3. Choice of the most adequate model
This part allows to choose the most adequate model de-
pending on inlet flow rate, temperature and pressure used.
In order to realise this part, the results calculated with
the software with the four models were compared with ex-
perimental data found in the literature [9–18]. The range

Table 10
Limiting values of the experimental conditions
Minimal value Maximal value
P (bar) 1 15.6
T (K) 293 1300
Density (kg/m3) 860 3900
Dc (m) 0.023 0.4
Volumetric flow rate (m3/s) 0.00005 0.25
Charge load (g/m3) 0.8 10
Table 11
Other geometries
Other geometry a/Dc b/Dc Ds/Dc Di/Dc H/Dc L/Dc h/Dc
Geometry 1 0.5 0.25 0.25 0.5 3.98 1.06 1.99
Geometry 2 0.38 0.19 0.38 0.31 4.31 1.13 1.81
of the experimental conditions used in these references is
summarised in Table 10. The other geometries used in the
software are summarised in Table 11.
3.1. Definition of the cut size
3.1.1. Evolution of the cut-size with inlet flow rate
The flow rate influences strongly the results as indicated
by several reports: Mothes and Löffler [12], Ray et al. [11],
Patterson and Munz [9] and Xiang et al. [15]. The tangen-
tial velocity increases with an increase of the inlet veloc-
ity, leading to a greater degree of separation in centrifugal
separators. Therefore, the cut-size decreases with increasing
flow rate.
Fig. 5 shows an example of cut-size variation with inlet
velocity according to Patterson and Munz [9]. It appears that
for inlet velocity higher than 5 m/s, the models of Lorenz and
Mothes and Löffler predict quite well experiments’ results.
Fig. 5. Evolution of cut-size with inlet velocity. Comparison between
experiments made by Patterson and the results obtained with the four
models (P = 1 bar, T = 293 K, d = 3900 kg/m3, Dc = 0.102 m, geometry
1 (Table 11)).
Fig. 6. Cut-size as a function of temperature. Comparison between ex-
periments made by Parker et al. [10] and the results obtained with the
four models (P = 1.9 bar, d = 2300 kg/m3, ui = 1.77–2 m/s, Dc = 0.058
m, geometry 2 (Table 11)).
This result is confirmed by the comparison made with data
of the other authors. However, at an inlet velocity below 5
m/s, Fig. 5 shows that the model of Leith and Licht gives
better predictions. The other authors do not work at such
low inlet velocities.
3.1.2. Evolution of the cut-size with the temperature
Cyclones are often used industrially at high temperature,
but unfortunately, the experimental studies realised in labo-
ratories are made at room temperature and there is a lack of
data concerning experiments at high temperature. However,
the work of Patterson and Munz [9], and Parker et al. [10]
present high interest.
The cut-size increases significantly with temperature. Ac-
cording to Fig. 6, the model of Mothes and Löffler gives
a good estimate of the cut-size for temperature below 450
K. At temperature higher than 450 K, the model of Lorenz
gives better predictions.
3.2. Study of pressure drop
3.2.1. Evolution of pressure drop with inlet flow rate
The articles of Patterson and Munz [9] and of Mothes and
Löffler [12] were used. It appears that accuracy of results
is highly dependent on values of inlet flow rate. Pressure
drop increases with flow rate. Even if a higher flow rate
tends to improve the separation, it is not relevant to work
at very high flow rate, because of the important increase
of pressure drop. In the case of a small inlet flow rate, the
model of Barth [1] gives the best result. However, at higher
flow rate, the model of Lorenz and Mothes [12] yields better
results.
Fig. 7 shows an example of pressure drop variation with
inlet flow rate (Patterson and Munz).

Fig. 7. Evolution of pressure drop with inlet flow rate. Comparison
between data presented by Patterson and Munz and the predictions of
the four models (P = 1 bar, T = 293 K, d = 3900 kg/m3, Dc = 0.102 m,
geometry 1 (Table 11)).
3.2.2. Evolution of pressure drop with temperature
The pressure drop decreases significantly with rising tem-
perature. This effect is mainly due to the decrease of the
density and the increase of the viscosity of the gas.
According to Fig. 8, the models of Barth and of Lorenz
give quite a good approximation of the pressure drop. How-
ever, Barth’s model does not take into account temperature
in its calculations: its predictions are, therefore, not reliable.
Using the data of Patterson and Munz, the four models are
equivalent, with an error in the prediction of about 80%.
3.3. Study of separation efficiency
3.3.1. Evolution of separation efficiency at room conditions
Separation efficiency at room temperature was studied us-
ing experimental data of Yoshida et al. [13], Xiang et al.
Fig. 8. Pressure drop as a function of temperature. Comparison between
data presented by Parker et al. [10] and the predictions of the four models
(P = 1.9 bar, d = 2300 kg/m3, ui = 1.77–2 m/s, Dc = 0.058 m, geometry
2 (Table 11)).
Fig. 9. Separation efficiency results. Comparison between data presented
by Ray et al. [11] and the predictions of the three models (Barth’s model
does not calculate efficiency, P = 1.7 bar, T = 293 K, d = 2640 kg/m3,
ui=11 m/s, Dc = 0.4 m, Stairmand geometry).
[15], Dietz [16] and Ray et al. [11] reports. They all show
that the model of Mothes and Löffler and of Lorenz yield
excellent predictions at inlet flow rates higher than 10 m/s.
An example of this agreement is presented in Fig. 9. How-
ever, for smaller flow rates, even if they stay the best models,
results are less precise.
3.3.2. Evolution of separation efficiency at high
temperature
Parker et al. [10] led experiments at temperature up to
973 K and pressures up to 25 bars. They concluded that the
efficiency decreases dramatically as temperature increases
from 293 to 993 K.
In order to verify the accuracy of model predictions, the
program was run under the same running conditions for the
three models. One set of results is presented on Fig. 10. It can
Fig. 10. Separation efficiency. Comparison between data of Parker et al.
[10] and the predictions of the three models (P = 1.9 bar, d = 2300 kg/m3,
ui = 1.97 m/s, Dc = 0.058 m, geometry 2 (Table 11)).

Fig. 11. Evolution of separation efficiency at high pressure. Comparison
between data by Parker et al. [10] and the predictions of the three models
(P = 5.16 bar, T = 293K, d = 2300 kg/m3, ui = 1.4 m/s, Dc = 0.058 m,
geometry 2 (Table 11)).
be seen that only Lorenz model gives a good prediction of
experiment values. This is hardly surprising since Lorenz’s
model is the most developed model of the software in terms
of temperature influence.
3.3.3. Evolution of separation efficiency at high pressure
According to the last part, the effect of pressure on ef-
ficiency results depends on the temperature chosen for the
experiment. Two cases are also distinguished: room temper-
ature and high temperatures.
3.3.3.1. Room temperature. Parker et al. [10] present data
obtained at room temperature and pressure higher than 2
bars. Fig. 11 presents four experiments realised under these
conditions. This experiment shows that the model of Leith
and Licht yields the better predictions.
3.3.3.2. High temperature. The data presented by Dietz
[16] concern experiments at temperature above 1000 K It
appears that the model of Leith and Licht gives here also
the best agreement with experiment (Fig. 12a). However,
for temperature around 780 K, the model of Lorenz gives
the best result (Fig. 12b). According to results of Parker
et al. [10] predictions at high temperature are better at high
pressure.
3.4. Domain of reliability of the models
Considering the work presented above, conclusions
may be drawn that help to choose the best model de-
pending on the operating conditions. Tables 12 and 13,
based on all the conclusions extracted from this study, in-
dicate for each experimental condition, the most reliable
models.
Fig. 12. (a) Evolution of separation efficiency. Comparison between data
by Dietz [16] and the predictions of the three models (P = 6 bar, T = 1221
K, d = 2500 kg/m3, ui = 49.4 m/s, Dc = 0.2 m, Swift1 geometry). (b)
Evolution of separation efficiency. Comparison between data of Parker
et al. [10] and prediction of the three models (P = 5.16 bar, T = 785 K,
d = 2300 kg/m3, ui = 1.98 m/s, Dc = 0.058 m, geometry 2 (Table 11)).
Table 12
Comparison of models predictions at different flow rate at room temper-
ature (T = 293 K)
Inlet flow rate, 5 m/s Inlet flow rate, 5 m/s
Separation efficiency Lorenz Lorenz
Mothes Mothes
Leith and Licht
Cut-size Leith and Licht Lorenz
Mothes
Pressure drop Barth Lorenz
Mothes
Table 13
Comparison of models predictions at different pressure and high temper-
ature
293 T 900 K T 900 K
Pressure 2 bar Pressure 2 bar
Separation efficiency Lorenz Lorenz Leith and Licht
Cut-size Lorenz Lorenz Leith and Licht
Leith and Licht Mothes
Pressure drop Lorenz Lorenz Lorenz
Mothes
Leith and Licht

4. Conclusion
The software cyclone presented in this paper offers an
easy way to calculate efficiency of a cyclone for a known
geometry or to choose geometry for a desired efficiency.
Four calculation procedures for aerocyclone design are
used in this software. Studies of literature cases, show that
models used in the software predict pretty well the exper-
imental results. Moreover, a comparison of the results ob-
tained with these four models permits to propose the model
the most adapted to an operating condition.
Some improvements could be done in the future to make
the software more efficient:
• by integrating a solid concentration term: indeed, calcu-
lations were made for solid concentration below 10 g/m3
of gas. If the solid loading exceeds a certain amount, ap-
proximately 10 g/m3, the gas stream is unable to carry
all particles. The exceeding solids are moving as a strand
directly into the dust chamber. To consider this effect
Muschelknautz and Brunner [18] introduced the so-called
‘limited solids loading µGR’ which could be integrated in
the software.
• By introducing new models: the models of Dietz [16] and
Zenz [19], developed in 1981 and 1984, could be added
and also the corrections of Clift (see Ghadiri and Hoffman
[20]) on the Leith and Licht model in 1991. These three
models proved efficient in several works [11,17].
Acknowledgements
The authors are very grateful to Dr. Patrick Yax from Sys-
matec for his help during the development of the software.
Appendix A. Nomenclature
A width of inlet cross-section (m)
B height of inlet cross-section (m)
ci particle concentration in the region I (kg/m3)
Ci(z) particle concentration at height z and
in the region i (kg/m3)
cw drag coefficient (–)
dp particle diameter (m)
dpc cut-size diameter (m)
Dc cyclone diameter (m)
Di outlet diameter for the gas (m)
Dturb diffusion coefficient (m2/s)
f correction factor (depending of the type of pipe)
g acceleration of gravity (m/s2)
G factor describing the geometric configuration (–)
heq equivalent height of the cyclone (m)
H total height of the cyclone (m)
ji(z) particle flux at the height z and
in the region i (kg/m2 s)
L engagement length of cyclone (m)
mw re-entrained flow (kg/s)
n vortex coefficient (–)
R radius (m)
Rc cyclone radius (m)
R∗
c radius of the cylindrical part for
the equivalent cyclone (m)
Re inlet radius of cyclone (m)
Ri gas outlet pipe radius (m)
R∗
i equivalent radius of the engagement
length of cyclone (m)
Rα average length from the entry to the centre (m)
Re Reynolds number (–)
Se cross surface area of the cyclone inlet (m2)
S cross surface area of the vortex finder inlet (m2)
Stot inner area of cyclone (m2)
T temperature (K)
u tangential velocity (m/s)
V volumetric flowrate at the abscissa z (m3/s)
V volume where the vortex turns (m3)
Vcyclone volume of the cyclone (m3)
V0 inlet volumetric flow rate (m3/s)
Vs secondary volumetric flow rate (m3/s)
ws settling velocity (m/s)
wr radial velocity (m/s)
W flow resistance force (N)
z axial co-ordonate (–)
Z centrifugal force (N)
Greek letters
α correction factor for contraction (–)
δ thickness of the boundary layer (m)
ε angle between the conical wall
and the vertical (–)
ζe pressure drop from the flow losses
through the outlet pipe (Pa)
ζi pressure drop from the inlet losses
and friction losses (Pa)
p pressure drop (Pa)
λ friction factor (–)
η separation efficiency (–)
ρ gas density (kg/m3)
ρp solids density (kg/m3)
τ relaxation time (s)
µ viscosity (Pa s)
θ angular momentum parameter (–)
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