Parvareh2011 PDF
Parvareh2011 PDF
Parvareh2011 PDF
Abstract This paper reports a study on the role of fluid flow pattern and dynamic pressure on the permeate flux
through a micro filtration membrane in laboratory scale. For this purpose, a dead-end membrane cell equipped with
a marine type impeller was used. The impeller was set to rotate in the clockwise and counter clockwise directions
with the same angular velocities in order to illustrate the effect of rotation direction on permeate flux. Consequently,
permeate fluxes were measured at various impeller rotational speeds. The computational fluid dynamics (CFD) pre-
dicted dynamic pressure was related to the fluxes obtained in the experiments. Using the CFD modeling, it is
proven that the change in dynamic pressure upon the membrane surface has direct effect on the permeate flux.
Keywords membrane, microfiltration, computational fluid dynamics, modeling, permeate flux
pressures as well as various cell setups, including a sidered as the novel point of this work.
cell equipped with three types of barrier and the same
cell without any barrier, were predicted. They com- 2 THEORY
pared the CFD prediction results with a simple calcu-
lation based on the well-known Darcy equation.
Ghidossi et al. [13] reviewed the studies on using Microfiltration is one of the most general mem-
CFD to model membrane separations and showed that brane separation processes. In general, two types of
CFD can provide interesting and important informa- fluid movement regimes are reported, dead-end and
tion for the development of membrane processes. cross flow. The driving force in the microfiltration is
Ranade and Kumar presented a detailed fluid hydro- the pressure gradient across the membrane. The Darcy
dynamics of spacer-filled channels using the “unit equation is the most general equation used in literature
cell” approach [14]. The CFD modeling was used to for determination of permeate flux, which is defined as
evaluate the performance of certain spacer shapes and 1 dV 'P
compare the results in flat and curved channels. Torras J (1)
A dt P ( RM Rc )
et al. [15] simulated a rotating disk flat membrane
module operated at high rotation speeds in the turbu- in which 'P is the transmembrane pressure, μ is the
lent regime using CFD technique and concluded that viscosity, RM is the membrane resistance, and Rc is the
the discrepancy for the membrane shear stress is proba- cake resistance.
bly due to an incorrect choice of Reynolds number for In the present study the fluid movement upon the
deducing the approximate solution. In another study, membrane surface is produced by a marine type im-
Alexiadis et al. [16] performed experimental and nu- peller, the impeller should be modeled similar to that
merical analyses for a reverse osmosis (RO) module in mixing tanks, which is the most important part for
and compared the results in order to validate the modeling a mixing tank. The three popular approaches
model from a practical perspective. They showed that for modeling an impeller are: impeller boundary con-
as 'P increased, the error between the CFD calcula- dition, inner-outer iterative procedure and sliding-grid
tions and experimental results increased. In a more method. In the impeller boundary condition method,
recent study, Pak et al. [17] simulated a laminar fluid which is the most traditional approach, steady condi-
flow in a 2D porous tube as a cross flow micro filtra- tions are imposed and simulations are conducted in
tion tubular membrane using CFD technique and de- the reference frame. This method needs empirically
veloped a numerical finite volume code, using SIM- derived boundary conditions, so the simulation results
PLE algorithm, for the solution of flow and concen- are strongly dependent on the predefined boundary
tration fields. conditions. The inner-outer method takes the approach
In the present study, the effects of fluid flow pat- just one step further. In this approach, the whole vessel
tern on the permeate flux through a microfiltration volume is subdivided into two partly overlapping re-
membrane are investigated. Two flow pattern regimes gions, as shown in Fig. 1 (a), an “inner” domain con-
are produced using a marine type impeller placed in- taining the impeller and an “outer” one containing the
side a dead-end cell. The main idea in this study is to rest of the tank. A crucial feature of this approach is
illustrate in what extent the flow pattern upon the the overlap region, common to the “inner” and “outer”
membrane surface is important. The flow pattern is domains, which provides the iterative matching of the
related to dynamic pressure, which is a part of total two solutions. The extent of this region and the exact
pressure upon the membrane surface. The dynamic location of its boundaries are largely arbitrary. By con-
pressure distribution is to be obtained by CFD model- trast, in the multiple frames of reference (MFR) method
ing. A scientific illustration of the importance of dy- [18], the “inner” and “outer” steady-state solutions are
namic pressure beside the static pressure can be con- implicitly matched along a single boundary surface
(a) Flow domain with overlapping region (b) Flow domain with common boundary
Figure 1 Different subdivisions of flow zones in a mixing tank [20]
20 Chin. J. Chem. Eng., Vol. 19, No. 1, February 2011
are fluctuation components, and U uicu cj is the aver- In order to investigate the effect of the fluid flow
aged Reynolds stress. on the membrane permeate flux, a dead-end cell
As the layout studied is an open surface case, the equipped with a mixer was used. In practice, the shear
system is involved with the contact of water and air. on the membrane surface is usually induced by a
Therefore, in Eq. (3), the density (ȡ) and viscosity (ȝ) spacer or rotating disk. In the present work, the shear
induced by an impeller is merely to illustrate the effect
of the fluid depend on the volume fractions of each
of fluid flow pattern on the membrane permeates flux.
phase and are calculated by the following equations Fig. 2 shows a schematic of the experimental cell and
U DUair (1 D ) U water (4) the place of the membrane and the impeller. The cell
consists of a glass cylinder with a height of 15 cm and
DUair Pair (1 D ) U water P water a diameter of 6.6 cm. The cell is fixed inside a frame
P (5) with a hole at the top and another at the cell bottom
DUair (1 D ) U water
for collecting permeate. The impeller is located at a
where D is the air volume fraction in the cell. The in- clearance of 9 cm from the cell bottom where a 5 cm
terface between two phases is tracked by the volume circular membrane sheet is placed.
fraction. Conservation of D can be represented by the The microfiltration membrane used in the current
interface mass balance, experiment was a hydrophilic Millipore PVDF (poly
vinylidene fluoride) with the commercial name of
wD GVWP. This membrane has a thickness of 120 μm
U D 0 (6)
wt and a porosity of 60%. The average pore size of the
membrane is 0.022 μm.
The cell phase is gas when D 1 , while D 0 means In order to eliminate the blocking effect due to
that the whole volume is occupied by the liquid. It can the formation of the cake on the membrane surface,
be concluded that the gas-liquid interface exists in the the cell was filled with deionized water up to 15 cm.
regions that D lies between zero and one. Physical properties of deionized water are considered
In addition to the above equations, the equations as those of water. Since the membrane resistance de-
of the RNG k-İ model are as follows [21, 22] pends on operating pressure, its value was measured
w( U k ) w w § Q eff wk · under the experimental condition. From the mass of
U ui k ¨ U V wx ¸ U Pk H (7) permeate obtained at different pressures in the range
wt wxi wxi © k i ¹ of experiments, the membrane resistance was obtained.
Chin. J. Chem. Eng., Vol. 19, No. 1, February 2011 21
flow fields in the vertical slice through the middle of rine impeller rotates in the counter clockwise direction
the impeller shaft are shown in Fig. 8, which reveals (b), the flow pattern consists of a loop in each side of
significant differences between the flows generated by the impeller. Thus the impeller pushes the fluid
the marine impeller in clockwise and counter clock- downward along the cell wall and after it hits the bot-
wise rotation. When the impeller rotates in clockwise tom most of the fluid goes up and returns to the im-
direction (a), the impeller pushes the water toward the peller. This flow pattern does not have a significant
bottom of the cell and after the fluid hits the mem- positive effect on pushing the water toward the mem-
brane surface, it moves upward along the cell wall. In brane surface. Therefore, it can not be expected that
this layout the water is pushed on the membrane sur- this layout is effective for increasing the permeate.
face, increasing the dynamic pressure in downward Figure 9 shows a 3D view of the region with the
direction upon the membrane surface. When the ma- axial downward velocity in the range of 0 to 0.13 m·s1.
24 Chin. J. Chem. Eng., Vol. 19, No. 1, February 2011
In the clockwise setup, the downward flow starts from cates that at higher speeds the effect of rotation speed
the impeller and goes toward the membrane surface at and consequently the effect of Reynolds number are
the bottom of the cell. For the counter clockwise mo- highly considerable. A similar trend is observed in the
tion of the impeller, the fluid moves downward only in experimental results of Fig. 6.
a small region around the impeller. Therefore, in the
clockwise setup, the downward stream causes a higher 6 CONCLUSIONS
dynamic pressure upon the membrane surface. This is
the main reason why more water passes through the
membrane in clockwise layout. In the present work, an experimental set up was
In the second step, the effect of rotation speed on designed to illustrate the importance of the fluid flow
the fluid flow with clockwise impeller rotation is dis- pattern and established dynamic pressure on mem-
cussed. Fig. 10 shows the average values of predicted brane flux. The experimental results show that two
dynamic pressure at different downward distances different flow patterns produced by an impeller, rotat-
from the impeller at various values of Reynolds num- ing in the clockwise and counter clockwise directions,
ber. The pressure increases slightly with increasing cause a significant difference on the permeate flux.
distance between the impeller and the cell bottom. In The permeate fluxes with the clockwise rotation in
addition, as the Reynolds number increases, the differ- some cases are more than three times of those with the
ence between the predicted pressures is larger, espe- counter clockwise rotation. In order to illustrate the
cially as the Reynolds number increases from 5410 to effect of dynamic pressure on the permeate flux, some
5830 r·min1. This pressure increases from about 96 to experiments were performed at several rotation speeds
125 Pa, which means that an 8% increase in the rota- (different Reynolds numbers) in the cell. It was ob-
tion speed causes about 23% increase of this pressure. served that as the rotation speed increases the perme-
The trend of pressure change is similar to the curve in ate flux increases.
Fig. 5 from the experiments, which shows that more Prediction of dynamic pressure distribution in-
permeate is collected at higher Reynolds numbers. side the cell is the main contribution of computational
fluid dynamics (CFD) modeling in this study. It is
tried to show the importance of dynamic pressure be-
side the static pressure in microfiltration membrane
separation. By analyzing the experimental and CFD
predicted results it is found that higher dynamic pres-
sure results in more membrane permeate fluxes. In the
other words, the results reveal a direct relation between
the flux and dynamic pressure. Thus a designer should
pay more attention to dynamic pressure as a part of
total pressure across a microfiltration membrane.
ȡ density, kg·m3 12 Rahimi, M., Madaeni, S.S., Abbasi, K., “CFD modeling of permeate
ı k, ı İ turbulent Prandtl numbers for k-İ flux in cross flow microfiltration membrane”, J. Membr. Sci., 225
Subscripts (1-2), 2331 (2005).
13 Ghidossi, R., Veyret, D., Moulin, P., “Computational fluid dynamics
i, j component
applied to membranes: State of the art and opportunities”, Chem.
Eng. Process., 45 (6), 437454 (2006).
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