condition which permits only the dispersed air bubbles to escape but
not the liquid phase [10,21,60]. On the walls, a n o-slip condition is
used for the liquid phase and a free-slip condition for the gas phase
[60,65,66,84]. Although the numerical results obtained from the free
slip boundary condition are approximately the same as that of the no
slip boundary condition [62], several numerical studies used the free
slip boundary condition for the gas phase. In reality, the bubble experi-
ences no fraction from the wall and it moves freely along the boundary.
Therefore, we can assume that direct contacts between the bubbles and
the walls are negligible [84]. In this case the velocity component parallel
to the wall has a finite value. In contrast, both the velocity normal to the
wall, and the wall shear stress are set to zero [62].
2.5. Numerical methods
The commercial CFD software package of ANSYS-CFX 13.0 is
employed for the current CFD investigation. There are several software
packages (e.g., ANSYS CFX, ANSYS Fluent and OpenFOAM) to simulate
fluid flow problems. ANSYS CFX is commonly used as high performance
software to p redict a wide range of fluid flow problems, particularly
simulation of multiphase flow (two or three phase). This software pro-
vides a complete suite of models i.e., Eulerian–Eulerian and a Lagrangian
particle tracking multiphase model to predict the interaction between
multiple fluid phases such as gases (bubbles) and liquids [10–13,21].
It can predict the homogeneous gas and liquid interaction where bubbles
have almost the same diamete rs and velocities [11–13] while it esti-
mates the heterogeneous flow regime where bubble sizes and velocities
change due to coalescence and break-up [10].
In the current CFD study, the control volume method is used to
discretize the conservation equations inside the bubble column. In CFD
simulations, there are several solution methods (such as finite difference
[85], Lattice Boltzmann [86–89], finite volume method [9,11–13,73])to
solve fluid flow problems. The most robust, reliable and the one on
which CFX is based is called the finite volume discretization method. In
this method, the domain of study is divided into subdomains which are
called control volume. All equations are discretized and iteratively solved
for each control volume. The discretization method of finite volume
is widely used to solve different physical problems in engineering
i.e., single and multiphase fluid flow and heat and mass transfer, especial-
ly fluid
flow
in bubble column reactors [1,2,9,11–13 ,73, 74].Itcancalcu-
late the structured or unstructured meshes and arbitrary geometries,
resulting in a robust scheme for simulations. In comparison to other nu-
merical methods, it can be more adequate to solve complex problems, es-
pecially chemical reaction and multiphase flow inside the bubble column
reactor. The equation system is solved using the SIMPLEC procedure. The
high order differencing schemes of the total variation diminishing (TVD)
are used, which is suggested for the Eulerian–Eulerian multiphase
models to reduce numerical diffusion [11,12,90]. The total variation
diminishing (TVD) scheme provides an accurate numerical solution
for the simple and complicated fluid flow problems with the existence
of discontinuities in flow field, particularly multiphase interaction due
to a robust calculation procedure. This model is commonly used to en-
hance flow pattern and gas dynamics results inside multiphase bubble
column reactors [11,12,79,90,91]. Using higher order discretization
order schemes i.e., total variation diminishing (TVD) scheme leads to a
decrease in the numerical diffusion and dispersion in the Eulerian frame-
work, resulting in accuracy in numerical results. This scheme with such
qualitative stability resolves discontinuities in the solution without spu-
rious oscillations which are usually represented by CFD solutions.
The bubbling process is simulated for 1400 s and all results are time
averaged over the last 1300 s. In order to test the sensitivity of the time
step on the accuracy of CFDresult, the time step of 0.1–0.01 is examined,
resulting in a small difference on the prediction of bubble column hy-
drodynamics. In this study the time step of 0.1 is used for all CFD studies.
2.6. Adaptive neuro-fuzzy application
2.6.1. Neuro-fuzzy computing
Soft computing is a way in the construction of systems that are com-
putationally smart. It transforms linguistic concepts to mathematical or
computational format for several complicated problems. This method
can also adapt in changing environments and learn to estimate the be-
havior of many uncertain processes. There is an advantage to applying
computing techniques together in a synergistic way rather than using
a system with one computing method. The finding of such synergistic
use of computing methods is the development of hybrid intelligent sys-
tems. The neuro-fuzzy computing method is one of the techniques that
are built as a result of intelligent system construction. At the beginning
this method detects system patterns by neural networks and then fuzzy
inference systems implement decision. As these two methodologies
merge together, they can build a novel method to recognize and proper-
ly predict a problem. This new system has an excellent ability to learn
from physical problems and adapt when the condition changes.
2.6.2. Adaptive neuro-fuzzy inference system
Fuzzy logic systems can be employed to convert linguistic concepts
to mathematical and computational architecture but they inaccurately
detec t and learn physical processes, changing boundary conditions.
Fig. 1. Grid intensity of the current CFD study consisting 40,500 structural elements.
469M. Pourtousi et al. / Powder Technology 274 (2015) 466–481