(559e) Geometric Optimization of Cyclones for Combination of Nonlinear Mathematical Programming and Computational Fluid Dynamics Techniques (CFD)

Abstract - The objective of this work
is to propose a new methodology to optimize the geometrical characteristics of
the cyclone separator to operate with high collection efficiency and low
pressure drop. The proposed method basically consists in coupling the CFD code
CYCLO-HEXA, ?in-house? simulator of gas-solid flows in cyclones developed
by Meier et al. (2011), in the optimization algorithm COMPLEX,
with nonlinear objective functions and inequality constraints. From the results
of CFD simulations, it is observed that the cyclones generated along the
iterations converge to a common geometry, due to the restrictions set forth in
the objective function, and this geometry gives the best results relative to
maximize the collection efficiency with lower pressure drop.

1.      INTRODUCTION

The
cyclones are widely used on separating particulate from a gas stream due to its
wide range of operation and simplicity in constructive form, which it makes a
device with a low investment cost and maintenance. However, it should be noted
that the collection efficiency of cyclones is directly related to operating
conditions and geometrical characteristics. Despite this simplicity, the fluid
dynamics of turbulent flow in cyclones is very complex, with various phenomena
including recirculation zones, high-intensity turbulent, high conservation of
vorticity, among others. Before the 1960's, the optimization methods and
equipment designs were empirical, based on experiments, intuition or
semi-empirical calculations, which were used in the similarity laws and testing
models. These empirical methods and semi-empirical, due to its simplicity, are
still widely used in the design and evaluation of various equipment used in the
industry, for example, cyclones. The objective of this work is develop a
methodology for optimizing the geometrical characteristics of the cyclone
separators, to operate with high collection efficiency and low pressure drop
through CFD techniques coupled with optimization methods.

2.      METHODOLOGY

The
proposed methodology basically consists in coupling of the simulator of
gas-solid flow in cyclones CYCLO-HEXA code, in the optimization
algorithm COMPLEX. The CYCLO-HEXA code is the result of
improvement of earlier versions developed by Meier (1998) in his Ph.D. work on
the development of a general model for the simulation of cyclones. The good
results obtained with the Eulerian-Eulerian model (MEIER and MORI, 1998; VEGINI
et al., 2008, MEIER et al., 2011) were crucial for this approach
was adopted as the standard in the CYCLO-HEXA code. The solid phase is
treated like a hypothetical fluid and drag forces between phases are
responsible for the gas-solid interaction. The CYCLO-HEXA code makes
possible the use of up to five solid phases, each one with size of particle,
density and specific volumetric fraction. The finite volume methods have been
used to discretize the partial differential equations of the model using the
SIMPLEC (SIMPLE Consistent) method for pressure-velocity coupling in a
3-D-space domain with a 3-D symmetric cyclone inlet. The modeling of turbulence
is formulated by combining the k-ε model for radial and axial components
of the Reynolds stress, and the mixture Prandtl theory for the tangential
components.

The
optimization algorithm COMPLEX used in this work, consists of maximizing
an objective function subject to inequality constraints (Fig. 1-a), that for
this case, means the maximization of the collection efficiency establishing a
maximum limit for the corresponding pressure drop. As variables, we chose five
of the eight basic geometric characteristics of a cyclone (Fig. 1-b), where
each of the five variables has a restriction for upper and lower limits.

Fig. 1.
(a) Objective functions subject to inequality constraints, where η is the
collection efficiency and ΔP is the pressure drop; (b) Geometrical
characterization of a cyclone.

The
optimization method consists in construct a geometric figure with a number of dimensions
at least equal to the number of manipulated variables more one. In this
particular case, we have five variables, and from there was chosen a
ten-dimensional optimization algorithm COMPLEX (twice the number of
variables). The generation of these ten points is conducted randomly by a
random number generator, where each point represents one different geometric
configuration of a cyclone according to Figure 2.

Fig. 2.
First iteration of optimization algorithm COMPLEX, where each point represents
the geometric configuration of the cyclone.

The
procedure starts with the generation of the initial condition, which
corresponds to the ten initial geometry of the first iteration of the system.
All of ten initial geometries are simulated through the CYCLO-HEXA code,
and results of collection efficiency and pressure drop are subjected to
evaluation of the objective function and constraints. The cyclones that present
the worst performance in terms of the objective function are discarded and a
new one is generated by the optimization algorithm COMPLEX. This
procedure is repeated until the objective function is maximized, while the
error or deviation of the iteration is minimized.

2.1.Operational
Conditions

As
a operational condition was used a gas flow of 220 m³/h at 180°C
with a loading ratio of 5000 mg of particles per m³ of gas (diluted flow).
The particulate system was analyzed using a Particle Size Analyzer by Laser Diffraction
Mastersizer S, S-MAM 5005 Model of the Malvern brand. Through the particle size
analysis, it was possible to obtain the diameter of the solid phases to the
desired fractions, as shown in Table 1.

Table 1.
Size of the particulate phase.

Where d_sn is the
average diameter to the solid phase n and the density (ρ_sn)
adopted for all solid phases is 1400 kg/m³.

3.      RESULTS
AND DISCUSSIONS

As
a first analysis, it is possible to verify the geometric evolution of cyclones
along the iterations, as shown in Figure 3, where the cyclone in blue had the
best performance of the interaction, while the reds color had the worst. The
cyclones that presenting the worst results of collection efficiency or higher
results of pressure drop will be dropped giving rise to a new geometry. Through
the Figure 3, it is possible to observe that the geometries of cyclones become
more similar along the iterations of the optimization process, confirming the
search for an objective function maximized.

Fig. 3.
Representation of geometric evolution of cyclones along the iterations.

It
is also possible to observe the maximization the objective function through
graphics of collection efficiency and pressure drop of individual cyclones of
the first and last iteration. In the first iteration (Fig. 4-a), it can be seen
a great variety of cyclones, some operating with a high collection efficiency,
and consequently high pressure drop, while others have very low efficiency of
collection, with pressure drops too low. This diversity was caused by the
random generation of cyclones within the geometric constraints imposed. However,
when analyzing the results obtained in the last iteration (Fig. 4-b), we can
see a great homogeneity of the results, besides maximizing the collection
efficiency with pressure drop within the constraints imposed on the method.

Fig.4.
Collection efficiency and pressure drop obtained in the first (a) and last (b)
iteration.

4.      CONCLUSIONS

From
the results presented in this work, it is possible to affirm that the proposed
methodology for the geometrical optimization of cyclones showed satisfactory
results within the operational limits established. It is also worth emphasizing
the importance of using CYCLO-HEXA code for simulation of cyclones,
because it presents reliable results at a computational cost much lower than
required by current commercial software, being possible to resolve  a large
number of experiments in a relatively short time, since the complete simulation
of each cyclone takes about 36 hours to complete in a personal computer.

REFERENCES

MEIER, H. F.; Modelagem
fenomenológica e simulação bidimensional de ciclones por técnicas da
fluidodinâmica computacional. Tese de Doutorado, UNICAMP, Campinas, São
Paulo, 1998.

MEIER, H. F.; MORI, M.; Gas-solid
flow in cyclones: The Eulerian-Eulerian approach. Computers & Chemical
Engineering, v. 22, n. Suppl., p. S641-S644, 1998.

MEIER, H. F.; VEGINI, A. A.; MORI,
M.; Four-Phase Eulerian-Eulerian Model for Prediction of Multiphase Flow in
Cyclones. The Journal of Computational Multiphase Flows, v. 3, p. 93-106,
2011.

VEGINI, A. A.; MEIER, H. F.; IESS,
J. J.; MORI, M.; Computational Fluid Dynamics (CFD) Analysis of Cyclone
Separators Connected in Series. Industrial & Engineering Chemistry
Research, v. 47, p. 192-200, 2008.