Computational Fluid Dynamics Modeling of High Viscous Feed Fluid in Rotating Corrugated Membrane Channel: Shear Stress Effect
Shear stress on the membrane surface has been proven very important in reducing concentration polarization and cake layer formation in membrane processes. This paper investigates the effect of rotation of membrane channels with high viscous feed solution on the membrane shear stress using Computational Fluid Dynamics (CFD). This study focus on two small membrane channels separated with corrugated spacer. The inner membrane was 39 mm and outer membrane was 41.5 mm from the axis of rotation. The feed solution viscosity used for the simulation was 0.0025 Pa•s and the inlet feed velocity was 2 m sec-1. The membrane shear stress is found out to be increasing with rotation speed. The shear stress on the outer membrane is also higher than inner membrane. There are three forces acting on the fluid flow in the membrane channels, namely pressure force, centrifugal force and tangential force. The rotation of the corrugated membrane channels can be applied to the spiral wound membrane module so that the membrane shear stress can be increased.
Received: February 08, 2011;
Accepted: April 11, 2011;
Published: December 16, 2011
Membrane application has widely been used in many industries. Furthermore,
many more researches on membrane is still on going to extend the membrane application
in various field (Abd El-Salam, 2006; Barakat,
2008; Ahmad and Chan, 2009). However, the main problem
facing by most of the membrane application, which is the membrane fouling, caused
by Concentration Polarization (CP) and cake layer formation is still under research
progress to solve the problem (Sakinah et al., 2007;
Zularisam et al., 2010). High shear stress on
the membrane surface is proven can reduce CP formation (Bouzerar
et al., 2003). The high membrane shear stress is able to increase
the back transport of rejected solute on the membrane surface (Bian
et al., 2000) and prevented formation of CP and cake layer on the
membrane (Bouzerar et al., 2000; Akoum
et al., 2005).
High membrane shear stress has been successfully achieved by the introduction
of dynamic membrane. The dynamic membrane uses mechanical energy to move the
membrane to create high shear stress on the membrane surface (Jaffrin,
2008) and reduce CP even for high viscous feed solution (Bhattacharjee
and Bhattacharya, 2006). The feed flow velocity and membrane surface shear
stress can be decoupled with the dynamic membrane system (Beier
and Jonsson, 2006). The high membrane shear stress can extend the pressure
limited regime and enable the increase of pressure that can increase the permeate
flux (Ding et al., 2003). The permeate flux in
dynamic membrane system can also be related with the membrane shear rate (Petala
and Zouboulis, 2006). Thus, dynamic membrane can attain higher permeate
flux than conventional crossflow (Akoum et al., 2004)
and turbular (Al-Akoum et al., 2002) membrane
system at the same transmembrane system.
The shear stress on the membrane surface can be easily estimated and modeled using Computational Fluid Dynamics (CFD) technique. In this study, CFD software (Fluent v6) is used to study the effect rotation of the membrane channels on the membrane shear stress for high viscous fluid solution.
MATERIALS AND METHODS
FLUENT v6 was used for modeling and simulation in current work. In present
simulation, a fluid with viscosity of 0.0025 Pa•s was used to study the
flow characteristics. This fluid viscosity is chosen based on the experiment
performed by Da Costa et al. (1991), where the
Dextran solution which has the fluid viscosity of 0.0025 Pa•s was used
(Da Costa et al., 1991). The feed flow inlet
velocity was set as 2 m sec-1 for all simulation.
||Mesh and motion track of the small channel in the spacer (a)
front view (b) side view (c) motion track
The permeate flux in the membrane channels is assumed to be very small compared
to the feed flow velocity and thus the hydrodynamics in the channels is not
affected by the permeation through the membrane. This has enabled the membrane
to be treated as impermeable wall. The simulations were performed using unsteady
state laminar flow at ambient pressure. Dynamic mesh function was used to define
the dynamic motion of the mesh where the motions were defined using User Defined
Function (UDF). The UDF was written in C programming language using
predefined macro in the FLUENT solver. Macro Define_CG_Motion for
dynamic mesh was used in the UDF. The discretization of the governing equations
was performed using a segregated incompressible flow solver in which each governing
equation is solved separately. The velocity and pressure parameters would be
linked and solved by SIMPLE algorithm. In order to achieve higher order of accuracy,
second order upwind discretization schemes was selected to compute the momentum.
The front view and side view computational domain is shown in Fig. 1. The simulated domain was 1 meter in length, 2 mm in height and 4 mm in wide. The mesh size generated on the membrane surface is 8x10-5 m between each node. The distance of the Inner Membrane (IM) with the axis of rotation is 39 mm and the Outer Membrane (OM) is 41.5 mm. The x and y direction was the rotation direction and z direction was the direction of fluid flow from inlet to outlet. The motion track of the small channel is shown in Fig. 1.
RESULT AND DISCUSSION
The hydrodynamics in the membrane channels was solved by fluent using laminar
Navier-Stoke equations. Rotation speeds from 0 to 200 rad sec-1 are
simulated to study the effect of rotation on the membrane surface shear stress
when the higher fluid viscosity which is almost six times higher than water
||Graph of average shear stress against rotation speed
Time step of 0.0001 sec was used for all simulations. All the results shown
in Fig. 2 were taken after the average shear rate was not
changing with time.
The area weighted average surface shear stress was computed from IM and OM. Fig. 2 shows the average surface shear stress versus the rotation speed of the membrane channels. The rotation of the membrane channels affects the fluid flow in inner and outer membrane channels differently. The shear stress on the OM started to increase as the membrane channels is rotated but it only started to increase at rotation speed beyond 100 rad sec-1 on IM. However, the shear stress on OM did not increase at the rotation speed was beyond 150 rad sec-1 while the shear stress on OM is still increases with the rotation speed.
Membrane fouling and concentration polarization phenomenon was expected to
be reduced by the increase of shear stress on membrane surface. Bergen
et al. (2003) had studied the enhancement of spiral wound membrane
by operating in dynamic operation in a centrifugal membrane separation system.
Their experiments results showed that the membrane fouling was reduced when
the membrane module was operated under centrifugal mode. Besides, they also
found that the permeate flux obtained in dynamic condition was higher than static
condition. Furthermore, the dynamic condition successfully reduced flux decline
too. Their results had agreed with the finding in this work that the rotation
of spiral wound membrane module can increase the membrane shear stress and thus
reduce membrane fouling. In addition, Brou et al.
(2002) had investigated the performance of rotating disk membrane filtration
using similar feed solution with viscosity of 0.00262 Pa•s. They found
out that the permeate flux increased with the rotation speed of the disk. The
trend of permeate flux increase had further confirmed the increase of membrane
shear stress with the rotation speed.
Three main forces were affecting the fluid flow in the rotating membrane channels, namely centrifugal force, tangential force and pressure force as shown in Fig. 3a.
||Forces acting on the fluid flow in the outer and inner channel
(a) three forces acting direction (b) forces acting in corrugated spacer
The rotation has created the centrifugal force; tangential force exists due
to spacer wall and pressure force is supplied by the feed pump. The feed pump
constantly pumped the feed fluid across the membrane channels at the specific
flow rate and formed a strong pressure force that pushes the fluid to flow from
the inlet towards the outlet direction. Thus, the pressure force is always in
the direction from inlet to outlet direction. This is also the main force that
determines the shear stress created on the membrane surfaces like conventional
crossflow membrane filtration process.
The tangential force due to the corrugated spacer wall and centrifugal force
was created due to the rotation of the membrane channels. Centrifugal force
is always facing in the direction out from the axis of rotation. Thus, the centrifugal
force had significantly shifted the high velocity region in the laminar Poiseuille
flow to the outer side of the membrane channels. This is the reason the shear
stress on the OM was always higher than the IM. When the centrifugal force shifted
the high velocity region outwards, the effect on the OM and IM was different.
The high velocity region was shifted near to the OM but away from the IM as
shown in Fig. 3b. The shear stress on OM was greatly increased
as high velocity gradient is created near OM. The shear stress on IM was not
affected much from the centrifugal force as the high velocity region is shifted
away from the IM. Thus, the shear stress on OM was increased even at low rotation
speed but there was no effect for the IM.
Tangential force was created due to the corrugated spacer wall as the rotation started. The corrugated spacer wall exerted the force in the rotation direction as if a plate pushing the fluid. This was the critical force that increases the shear stress on the membrane surfaces. This force was able to increase the fluid flow velocity in the membrane channels and thus increase the velocity gradient near the membrane surfaces. Hence, the shear stress on the membrane was able to increase due to the existence of tangential force even for a fluid with viscosity almost six times higher than water. The effect of this force is significant beyond the rotation speed of 100 rad sec-1. The shear stress on IM started to increase significantly only when rotation speed was beyond 100 rad sec-1 because it was not affected by centrifugal force. Tangential is the only force that able to increase the shear stress on IM. This tangential force also helps to further increase the shear stress on OM.
However, the shear stress on OM was not increased when the rotation speed beyond 150 rad sec-1. This phenomenon happens because at rotation speed higher than 150 rad sec-1, the fluid flow velocity was not increased by the tangential force as much as the increase of OM instantaneous velocity. Since the fluid viscosity was higher than water, higher force is required to move the fluid as it has higher internal resistance. Thus, when the membrane channels were rotating at high speed, the tangential force created by the spacer wall was not able to increase the fluid flow velocity significantly. Anyhow, the increase of instantaneous velocity of IM was still lower than the increase of fluid velocity in inner membrane channel and caused the shear stress on IM was still in the increasing manner even rotation speed was exceed 150 rad sec-1. However, due to the centrifugal force that shifted the high velocity region outwards, the shear stress on the OM was still higher than IM when rotation speed was below 200 rad sec-1 although the shear stress did not increase with rotation speed.
The shear stress on the membrane surfaces for fluid with viscosity of 0.0025
Pa•s, which is almost six times more viscous than water, in the corrugated
spacer filled membrane channels is able to be increased by rotating the membrane
channels. The higher shear stress on membrane surface can reduce the concentration
polarization and cake layer formation on the membrane surface and further enhance
the membrane application. The shear stress is found out to be increase with
rotation speed of the membrane channels. The hydrodynamics in the rotating membrane
channels is governed by three forces, namely pressure force, centrifugal force
and tangential force. Pressure force is the main force that determines the shear
stress on the membrane surfaces. Centrifugal force is the force moved the fluid
flow high velocity region away from the axis of rotation and caused the difference
of shear stress on IM and OM. Tangential force is created by the corrugated
spacer wall which is the critical force that plays the important role to increase
the shear stress on the membrane surfaces in the rotating membrane channels.
This work was funded by the Grant PRGS by Universiti Sains Malaysia. The authors would also like to thank USM fellowship for giving financial support to Mr. Z.H. Ban.
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