Environment Protection Engineering
Vol. 42 2016 No. 3
DOI: 10.5277/epe160309
RYSZARD WÓJTOWICZ1, PAWEŁ WOLAK2
AN EXAMPLE OF THE USE
OF COMPUTATIONAL-FLUID-DYNAMICS ANALYSIS
FOR SIMULATION OF TWO-PHASE FLOW
IN A CYCLONE WITH A TANGENTIAL INLET
The feasibility of using a software package, based on computational fluid dynamics (CFD) codes
to simulate two-phase (gas–solid) flows in a cyclone with a tangential inlet was studied. The method-
ology of numerical simulations and calculations has been presented and the main parameters influenc-
ing the effectiveness of the cyclone elaborated. Findings are presented as contour maps of the distri-
bution of selected flow parameters (velocity, pressure) in some parts of the apparatus or as
visualizations of vortex formation structures and particle motion trajectories in the cyclone. The results
of simulation were compared with those based on literature correlations and experimental results of
laboratory tests.
1. INTRODUCTION
Cyclones constitute a large group of devices commonly used in many industrial
technologies. They are used for separation of solid particles from a dusty gas, mainly in
processes of environmental protection [1, 2], and also as final separation devices in
pneumatic transport systems. Cyclones have a simple and compact design, are devoid
of moving parts, and their universality and uncomplicated operation make them per-
fectly adapted to work in various, often adverse conditions such as high pressure and
elevated temperatures at variable humidity of polluted gas.
_________________________
1Cracow University of Technology, Faculty of Mechanical Engineering, Institute of Thermal and Pro-
cess Engineering, Aleja Jana Pawła II 37, 31-864 Cracow, Poland, corresponding author: R. Wójtowicz.
e-mail: [emailprotected] 2Air Liquide Global E&C Solutions, Poland S.A., Static Equipment Department, Mogilska 41, 31-545
Cracow, Poland.
110 R. WÓJTOWICZ, P. WOLAK
Despite the simplicity of construction of the cyclone, its gas flow profile is complex
and depends on several parameters, mainly influenced by geometry and dimensions of its
parts. An essential significance have also the shape and location of the inlet of polluted gas
and of an overflow pipe. Their accurate construction enables one to eliminate undesirable
phenomena occurring during the operation such as gas flow directly from inlet to outlet duct
of the cyclone (so-called short circuit), a violent contraction of the inlet stream or – impeding
dust removal - transferring vortex motion of gas to a reservoir of dust.
Computer simulation packages based on specially created codes of computational fluid
dynamics (CFD) [3–5] are useful tools commonly applied during computer-aided design of
industrial equipment. Their advantages such as the universality of application, ability to
quickly modify dimensions and geometry of a designed device and also broad possibility of
presentation of results make them useful during design and optimization of dust separators
including cyclones. An important advantage of their application seems to be the possibility
of modeling of multiphase flows – in the case of cyclones a two-phase flow (gas–solid par-
ticles), being crucial in optimization of constructions and in the estimation of pressure drops,
sizes of particles separated in the cyclone and effectiveness of its dedusting. Due to all those
advantages, CFD packages seem to be useful and helpful in the analysis of cyclone separa-
tors. However, not many papers have been published on this topic.
Elsayed and Lacor [6] using CFD simulations and Muschelknautz’s approach con-
ducted optimization of the cyclone geometry (the vortex finder diameter, inlet width
and height, and cyclone total height) for a minimum pressure drop. A new set of geo-
metrical ratios for a cyclone design was proposed. Safikani et al. [7] presented the re-
sults of CFD simulations of flow field in three types of cyclones, named 1D3D, 2D2D
and 1D2D. The length of the cylindrical part of the body is equal to 1, 2, and 1 the
body diameters, while the length of the conical part is 3, 2 and 2 the body diameters.
The authors analyzed velocities, static pressure and turbulence intensity distributions.
Predicted data were compared to experimental as well as theoretical values. The impact
of particle agglomeration on the collection efficiency of a cyclone was studied by Paiva
et al. [8] and a new model for prediction of the collection efficiency was proposed. The
maximum-efficiency cyclone length was found by Surmen et al. [9]. The authors, using
a theoretical approach based on cyclone geometry and fluid properties obtained a rela-
tionship describing minimum particle diameter or maximum cyclone efficiency.
Few papers only were published on CFD modelling of cyclone separators, com-
pared to many published studies on other industrial equipment, e.g. mixing vessels or
heat exchangers. Many papers lack a comparison between CFD-predicted results, theo-
retically calculated values, and measurements. Even if two-phase simulations were per-
formed – possibilities of CFD software for presentation of the results were relatively
poorly used. The papers lack visualizations of flow, vortices formation etc., created on
based on various defined criterions. In addition, the research lacks visualization of se-
lected trajectories of particles and analysis their collection in main part of a cyclone as
Simulation of two-phase flow in a cyclone with a tangential inlet 111
well as in a dust chamber, which can help in selection and optimization of a cyclone
design. The current state of research shows a need for further examination.
2. THE MECHANISM OF PARTICLE DEDUSTING IN A CYCLONE AND MAIN
PARAMETERS DETERMINING EFFECTIVENESS OF ITS PERFORMANCE
In cyclones for gas dedusting, a more efficient dedusting mechanism is used, based
on centrifugal forces acting on particles. A stream of a polluted gas is introduced tan-
gentially into a cyclone. Next, a dusty gas set in a rotational motion creates in a cyclone
the so-called the outer spiral with a diameter comparable to the cylindrical part of a
cyclone diameter. Centrifugal force acting on particles causes their gradual movement
in the direction of an apparatus wall and as a consequence, their collection. The purified
gas forms the so-called inner spiral (a small-scale vortex close to the cyclone vertical
axis) and escapes outside through the vortex finder. A centrifugal force which deter-
mines a particle dedusting process depends on the geometry and dimensions of the cy-
clone, particle size, and first of all on a tangential velocity of gas. For effective cyclone
performance, these quantities must be taken into account at the stage of its design and
during the choice of process conditions.
An analysis of motion of a dusty gas in a cyclone based on various models proposed
in the literature leads to a choice of two main parameters determining an efficiency of
cyclone performance, which are: pressure drop of gas flowing through a cyclone and
dedusting efficiency. The pressure drop of gas in a cyclone can be caused by many
factors, e.g. by gas frictional drags at an inlet and walls, also by energy losses during
gas decompression and turbulence inside a cyclone. The latter parameter directly deter-
mines the selection of devices supplying a dusty gas to a cyclone and their power re-
quirements, and therefore – which is important – energy expenditure for the whole pro-
cess.
Correlations for determining the pressure drop in cyclones have a similar form and
take into account an inlet gas velocity and geometry of an apparatus. This dependence
in a general manner can be written as:
2
Δ2
c
up (1)
where is a coefficient characterized by a cyclone dimension proportion, variously de-
fined by various authors.
Warych [2] characterized as the coefficient of local resistance (ξ) and recom-
mends to assume its value between 4.5 and 11.0, depending on the geometry of a cy-
clone. Casal and Martinez [10] on the basis of a statistical analysis of experimental data
propose a correlation in the form of:
112 R. WÓJTOWICZ, P. WOLAK
2
211.3 3.33
e
ab
D
(2)
Another equation to determine the coefficient was proposed by Shepherd and
Lapple [11]:
2
16e
ab
D (3)
co*ker [12] defined as:
2
9.47e
ab
D (4)
Typical inlet velocities of a dusty gas for a cyclone amount to 10–25 m/s [1, 2].
However, the highest ones with substantial concentrations of particles in the gas can
cause a strong erosion of the cyclone, in the upper, inlet part as well as in the lower,
conical one.
The other important parameter characterizing the effectiveness of a cyclone perfor-
mance is its dedusting efficiency . A classic relation for estimation of dedusting effi-
ciency can be written as:
100%s
i
m
m (5)
where: ms is a weight of dedusted (collected) particles, and mi is a weight of all particles
supplied to a cyclone with a polluted gas.
Another correlation was proposed by Leith and Licht [13]:
1/(2 2)2
1 exp 2 2( 1)
n
i i
un t
R
(6)
where: i is a response time dependent on a particle diameter, particle density and gas
viscosity, t represents an average residence time of gas depending on a gas inlet velocity
and cyclone geometry, n is the so-called vortex exponent, calculated from the following
equation:
0.3
0.141 1 0.669293
Tn D
(7)
Simulation of two-phase flow in a cyclone with a tangential inlet 113
Taking above into account and analyzing the previously described relation of parti-
cle deposition with the value of a centrifugal force acting on particles, we can state that,
dedusting efficiency will increase upon increasing particle diameter, their density and
tangential velocity, while decrease upon increasing radius of particle swirl in an appa-
ratus.
3. SIMULATION METHODOLOGY
Figure 1 presents a view, geometry and basic dimensions of the investigated cy-
clone. The diameter of the cylindrical part was D = 0.192 m, and the total height of the
cyclone H = 0.745 m. The inlet channel was square cross-sectional, with dimensions
a = b = 0.042 m and total length c = 0.2 m. The height of the cylindrical part of the
cyclone was h = 0.242 m, the diameter of the vortex finder De = 0.09 m and length of
the vortex finder inside the cyclone was s = 0.140 m. The diameter of the cyclone at the
end of the conical part was chosen to be B = 0.045 m.
Fig. 1. The cyclone investigated: a) a general view, b) geometry and overall dimensions
(z1–z3 – cross-section planes)
114 R. WÓJTOWICZ, P. WOLAK
The gas flowing through the cyclone was air (c = 1.225 kg/m3, c = 1.7894·10–5 Pa·s),
its velocity u at the inlet of the cyclone was changed in the range of 10–20 m/s. The ash
with density of s = 2700 kg/m3 was used as solid particles. The dispersed phase volume
fraction was relatively low, lower than 5%. During simulations, it was assumed that
particle size distribution is characterized by the Rosin–Rammler theoretical distribution
(Fig. 2), whose main parameters are listed in Table 1. All parameters of particles as-
sumed in simulations were the same as those in our laboratory tests used (verification
of simulations).
Fig. 2. Size distribution of applied particles
T a b l e 1
Main statistical parameters of particle population
Parameter Value
Total number of particles n 5.321×106
Minimum diameter dpmin 2 m
Maximum diameter dpmax 100 m
Mean diameter dpmn 24.7 m
Sauter mean diameter d32 51.5 m
Standard deviation 17.3 m
Spread parameter 2.537
The analysis of the two-phase (gas–solid) flow was performed based on results of
numerical modelling, using as a pre-processor the mesh generator Gambit 2.4. At the
pre-processing stage, model geometry was created, numeric mesh generated and bound-
ary conditions set. The numeric mesh consisted of about 3×105 tetrahedral cells. Mesh
quality was examined by means of EquiAngle Skew and EquiSize Skew criterions [14].
Their values showed that the mesh had a good quality.
Simulation of two-phase flow in a cyclone with a tangential inlet 115
Numerical calculations and the analysis of results were carried out using the Ansys Fluent
14.0 solver and CFD Post post-processor, respectively. The base for calculations of dis-
crete phase (particles) motion was the initial conditions, which determined the starting
positions, velocity and other parameters for each stream of particles and physical effects
affecting their stream. To simulate the motion of the discrete phase, the Euler–Lagrange
(EL) [3] approach was used. In this approach, a motion of the continuous phase (gas) is
modelled using the transport equations averaged over a computational cell and a discrete
phase (particle) motion by solving the equations of motion for each particle separately.
Turbulent gas flow in the cyclone was described mathematically using the Navier
–Stokes equations of mass and momentum transport, averaged further by the Reynolds
method (RANS) [5]. As a closing method, the renormalization group (RNG) k-turbu-
lence model was selected with an additional option of the swirl modification [15], taking
into account the mean flow vorticity – vortex formation during polluted gas motion in
our cyclone. The turbulence model complements with two basic equations such as equa-
tion of kinetic energy of turbulence k and that of the rate of energy dissipation De-
tailed information on the method for gas flow modelling in the cyclone, the turbulence
model and boundary conditions has been presented elsewhere [4].
4. RESULTS OF SIMULATION
Figure 3 presents visualizations of vortex formation for the selected gas flow veloc-
ity (u = 15 m/s). Visualizations were made on the basis of fixed values (iso-surfaces) of
Q-criterion, defined as [16]:
2 210
2Q S (8)
where: S is the rate-of-strain tensor and is the vorticity tensor.
The latter criterion was used to identify the cores of vortex structures, formed in the
cyclone. On the basis of that it is possible to determine location and scale vortices gen-
erated in the dusty gas, involved in the dedusting process.
The images show two different structures of vortices, forming in the cyclone during
gas flow: the main vortex (the outer spiral, where solid particles are separated) (Fig. 3a)
with scale (diameter) comparable to the cylindrical part of the cyclone diameter, and
a smaller-scale vortex (a stream of purified gas leaving the cyclone, the so-called inner
spiral, Fig. 3b) with a diameter close to that of the vortex finder, forming in the cyclone
center close to its vertical axis. Another interesting occurrence (Fig. 3a) was the for-
mation of a chaotic gas flow in the dust chamber which can cause re-entrainment of the
smallest particles that embedded earlier.
116 R. WÓJTOWICZ, P. WOLAK
Fig. 3. Visualization of vortices in the cyclone using the Q-criterion:
a) the outer spiral (Q = 0.45 s–2), b) the inner spiral (Q = 0.05 s–2, u = 15 m/s)
Fig. 4. Contour maps of gas velocities (m/s) in the cyclone for various inlet velocities:
a) u = 10 m/s, b) u = 15 m/s, c) u = 20 m/s
Simulation of two-phase flow in a cyclone with a tangential inlet 117
Fig. 5. Tangential component of flow velocity
in function of the cyclone radius and gas inlet
velocity: cross-section planes a) z1, b) z2, c) z3
Another interesting phenomenon observed during simulations is high gas flow ve-
locity at the connection of the inlet channel with the cylindrical part of the cyclone. Its
qualitative analysis is presented in contour maps shown in Fig. 4 and a quantitative
approach is illustrated in Fig. 5.
A detailed analysis shows that the reason for this may be a sudden narrowing of the
gas stream at the start of its rotational motion and a high increase of the tangential com-
ponent of velocity, crucial for a dedusting process. Its values can be higher than those
of the gas inlet velocity even by 30% (Fig. 5a). This tendency was observed for all tested
gas inlet velocities. It was reported and described elsewhere (cf. [4, 6]).
The analysis of curves illustrating changes of the tangential component velocity
along cyclone radius for selected cutting cyclone planes (z1 – inlet cross-section plane,
118 R. WÓJTOWICZ, P. WOLAK
z2 – cross-section plane in the zone of connection of a cylindrical part and conical ones,
z3 – cross-section plane in a half-height of conical part, Fig. 1) also showed that changes
for z1 plane are different from those, which are obtained for z2 and z3. In this first case
(Fig. 5a) we can see four maxima: two of them characterize the main flow in the cylin-
drical part of the cyclone, two characterize the flow in the vortex finder. The values of
the gas velocity vary by 30–35% for the main flow, probably due to an increase of the
flow velocity at the start of gas rotational motion. The values of the vortex finder max-
ima are comparable, pointing to a stable swirling flow in this zone.
For two other cross-section planes (Figs. 5b, c) profiles are very similar, differences
are observed only in figures. A distinct maximum of velocity close to the cyclone wall
is visible and its minimum in the vicinity of the cyclone vertical axis. This clearly indi-
cates the existence of previously shown flow pattern that plays a decisive role in a de-
dusting process and deposition of particles.
Fig. 6. Distribution of the static pressure (Pa) in the cyclone for various inlet velocities:
a) u = 10 m/s, b) u = 15 m/s, c) u = 20 m/s
Figure 6 shows a distribution of a static pressure in the cyclone for three gas inlet
velocities u – 10, 15, 20 m/s. The values and distribution of the static pressure in the
cyclone change substantially, depending on the gas velocity at the inlet. However, some
trends are similar. The highest values of the static pressure are observed in the upper,
Simulation of two-phase flow in a cyclone with a tangential inlet 119
cylindrical part of the cyclone, particularly close to its wall. The smallest ones are in the
cyclone interior, close to the axis. Narrow and relatively small zones of subatmospheric
pressure are visible in the upper part of the cyclone at the beginning of the vortex finder.
Based on the simulated values of the static pressure, a pressure drop in the cyclone
was calculated. It is one of the most important parameters characterizing cyclone per-
formance and its operation costs. The pressure drop was calculated as the difference
between the static pressures: at the inlet and in the vortex finder. Obtained results were
compared with those measured in a real dedusting installation with a cyclone of similar
geometry and dimensions (Fig. 1) [17]. A comparison of results is shown in Table 2.
T a b l e 2
Pressure drop for the examined cyclone [Pa]
Inlet
velocity
[m/s]
Pressure drop according to Eqs. CFD simulations
Measurements (1)
6 (1) and (2) (1) and (3) (1) and (4)
static
pressure
total
pressure
10 367 203 213 216 134 169 190
15 826 459 480 284 313 366 340
20 1470 820 854 505 564 649 580
The differences between the values of pressure drops predicted by CFD simulations
using static pressure values and those obtained from measurements were remarkably
small. For gas inlet velocities u = 15 m/s and u = 20 m/s, they did not exceed 8.5% and
2.8%, respectively. Bigger difference (ca. 40%) was visible only for the lowest gas inlet
velocity (u = 10 m/s) probably due to not sufficiently precise definition of the CFD
model of cyclone operating parameters. Consequently, inaccuracies in the mathematical
description of some geometrical quantities, e.g. sharp edges and surface roughness,
might have had a more expressive effect at such low gas speeds.
The pressure drops determined with different models and correlations proposed in
literature substantially differ. The highest values – significantly different from others
– were determined from Eq. (1) using relatively low values of the coefficient = = 6,
recommended for a cyclone of a similar geometry. The next two models (Eqs. (1) and (2),
as well as Eqs. (1) and (3)) produced quite similar pressure drops, with slightly higher
values than those of the approach described by Eq. (3). The lowest values of the pressure
drop in the cyclone were obtained using Eqs. (1) and (4). Because these models consider
the total (static and dynamic) pressure, for a better comparison, this quantity was pre-
dicted from simulations (Table 2). The smallest discrepancies between predicted and
calculated values gives the co*ker model (maximum differences do not exceed 28%) and
this model seems to be the most useful to predict the pressure drop in the analyzed cy-
clone.
120 R. WÓJTOWICZ, P. WOLAK
Figure 7 shows a visualization of a movement of hypothetical dust particles in the
cyclone at the inlet gas velocity u = 15 m/s. Trajectories of particles were analyzed for
three different particle diameters, 2, 20 and 100 μm. Particles were injected into the
cyclone in the central point of the inlet channel (the intersection point of the diagonals
of the square).
Fig. 7. Trajectories of particles of various diameters:
a) dp = 2 µm, b) dp = 20 µm, c) dp = 100 µm (u = 15 m/s)
The smallest particles (Fig. 7a) injected tangentially to the cyclone begin to move
the swirl motion, creating an outer spiral with a large diameter. They lose their velocity
as they come into contact with the wall in the cylindrical part of the apparatus. Next,
with a slow velocity and swirling motion, they slide down to the dust chamber. The
smallest particles are then re-entrained by the flow of the purified gas and with a swirl-
ing motion create an inner spiral, and eventually leave the cyclone along with the gas.
Larger particles, with a diameter dp of approximately 20 μm (Fig. 7b) embed at the
beginning of their movement and losing velocity with the spiral movement slide down
to the dust chamber. Although at the top part of the chamber we can observe disturb-
ances of their trajectories, they are separated from the polluted gas.
The largest particles (dp ≈ 100 m) as a result of their inertia strike a wall of the
cyclone already at the beginning of their movement (just after being inserted into the
Simulation of two-phase flow in a cyclone with a tangential inlet 121
cyclone), they can be reflected from the wall and next embed on the wall and slide down
with a spiral movement into the dust chamber (Fig. 7c).
The above-described mechanism is directly related to the second parameter that in-
fluences the effectiveness of cyclone performance – dedusting efficiency. Software used
in this study allows to monitor the number of particles: introduced, embedded and leav-
ing the cyclone along with the purified gas, for a specified range of their diameters.
Therefore, it is possible to calculate the mass of particles at the inlet and outlet of the
cyclone, and also those that embed in the dust chamber. These data were used to calcu-
late a dedusting efficiency of the cyclone, according to classic proportion (Eq. (5)). Re-
sults were compared to those calculated from a literature correlation (Eq. (6)) and those
measured in a real installation (processed with Eq. (5)). A comparison is presented in
Table 3.
T a b l e 3
Calculated and simulated dedusting efficiencies of the cyclone [%]
Inlet velocity
[m/s]
Efficiency of dedusting
According
to Eq. (6)
CFD
simulations Measurements
10 80.3 80.8 83.3
15 84.3 86.3 87.8
20 86.9 87 91.2
Regardless of the gas inlet velocity, the obtained results are very similar, and in
some cases almost identical. The maximum difference between simulated and calcu-
lated values does not exceed 2.3% and in the case of simulated and measured data is
slightly higher, reaching 4.8%. This indicates the high quality of used the numerical
model and its usefulness for determination of a dedusting efficiency of the cyclone.
5. CONCLUSION
The goal of the simulations was a numerical modeling of the two-phase (gas and
solid) flow in the cyclone with a tangential inlet. During investigations the usefulness
of the computer software to analyse cyclone performance was also examined. The re-
sults were compared with data calculated from empirical/literature correlations as well
as the results of our own measurements.
Qualitative and quantitative analysis showed a relatively good consistence between
data obtained from simulations, calculations and measurements. In the case of estima-
tion of the pressure drop, the smallest differences were obtained during the comparison
122 R. WÓJTOWICZ, P. WOLAK
of simulated and measured data with the co*ker model. However, in the case of dedust-
ing efficiency, simulated, calculated and measured data were almost identical, which
confirms the selection of the applied numerical model.
The simulations showed also that computational packages based on CFD codes are
a useful and effective tool which may be successfully used in the design and optimiza-
tion of cyclones. They allow quick and easy analysis of polluted gas flow inside a cy-
clone without time-consuming experimental tests and building of prototypes. Moreover,
with the use of CFD analysis we can also very quickly change and modify the geometry
of the cyclone in a wide range variability of process parameters and – in consequence
– improve the performance of apparatuses.
An inconvenience of the software used is its relatively poor database, including the-
oretical particle size distributions. This imposes some limitations in the use of CFD
analysis for the description of diameters and particle size distributions of some dusts
used in the industrial practice. Another disadvantage of used CFD software is its inabil-
ity to simulate the interaction among solid particles which restricts the use of the model
for a dusty gas with a low concentration of solid particles.
SYMBOLS
a, b – inlet height and width of the cyclone, m
B – diameter of the conical part, m
D – diameter of the cyclone body, m
c – length of the inlet channel, m
dp – particle diameter, m
dpmax – maximum particle diameter, m
dpmin – minimum particle diameter, m
dpmn – mean particle diameter, m
d32 – Sauter mean particle diameter, m
De – vortex finder diameter, m
h – height of the cylindrical part, m
H – cyclone height, m
k – turbulence kinetic energy, m2/s2
ms – mass of collected particles, kg
mi – mass of all particles introduced, kg
n – total number of particles
n – vortex exponent
r – cyclone radius, m
R – cyclone body radius, m
s – vortex finder length (inside the cyclone), m
S – rate-of-strain tensor, 1/s
t – time, s
Tp – particle temperature, K
u – gas inlet velocity, m/s
ut – gas tangential velocity, m/s
Q – Q-criterion value, 1/s2
Simulation of two-phase flow in a cyclone with a tangential inlet 123
z1, z2, z3 – cross-section planes
– cyclone dimensions coefficient
– spread parameter
p – pressure drop, Pa
– energy dissipation, m2/s3
i – dedusting efficiency, %
c – continuous phase viscosity, Pa·s
– local resistance coefficient
c – continuous phase density, kg/m3 s – density of solid particle, kg/m3
– standard deviation, m
i – response time, s
– vorticity tensor, 1/s
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