Effect of the baffle design and orientation on the efficiency of a membrane tube

chemical engineering research and design 1 1 7 ( 2 0 1 7 ) 500–508

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Chemical Engineering Research and Design journal homepage: www.elsevier.com/locate/cherd

Effect of the baffle design and orientation on the efficiency of a membrane tube Houari Ameur a,∗ , Djamel Sahel b a

Department of Technology, Institute of Science and Technology, Ahmed Salhi University Center of Naâma (Ctr Univ Naâma), PB 66, 45000, Algeria b Laboratory of Gaseous Fuels and Environment, Faculty of Mechanical Engineering, University of Science and Technology USTO-MB, PB 1505, El-M’Naouar, Oran 31000, Algeria

a r t i c l e

i n f o

a b s t r a c t

Article history:

A numerical investigation is carried out to examine the effect of a new baffle design in a

Received 19 April 2016

membrane tube on the hydrodynamics and filtration efficiency. Two different orientations

Received in revised form 22 October

of hemispherical baffles named as RO baffle for the Right Orientation and LO baffle for the

2016

Left Orientation, respectively, are explored. Two values of the carbonate calcium suspen-

Accepted 6 November 2016

sions are used: 5 and 10 g/L. The axial velocity, stream function, static pressure, wall shear

Available online 14 November 2016

stresses and turbulent characteristics are the physical parameters utilized to evaluate the

Keywords:

spherical baffles can develop the local shear stresses on the membrane surface and create

filtration performance. The obtained results showed that the presence of an array of hemiMembrane tube

the fluid eddy movement which enhances considerably the filtration performance. When

Baffle design

the feed concentration is 5 g/L and in a comparison with the unbaffled tubes, the RO and

Hemispherical baffle

LO cases achieved an increase in the filtration flux rate by 57% and 64%, respectively. For

Filtration

the second feed concentration (10 g/L), the enhancements are 85% and 96% for the RO and

Turbulent flows

LO cases, respectively. In a comparison between the LO and RO cases, the LO baffle gives the best performance. Our results were compared with experimental data and a satisfactory agreement has been found. © 2016 Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved.

1.

Introduction

The membrane tubes are widely used in several industrial processes, such as water treatment, removal of heavy metal, desalination and other industrial fields. However, the major problem in using the membrane tube in these processes is the concentration polarization, which reduces the filtration flux due to the formation of the hydrodynamic boundary layer, resulting then in the formation of a gel on the membrane surface. Baffles or turbulence developers inside the membrane tube are considered as a very successful technique to enhance the filtration flux. These geometrical configurations help to stop the appearance of the boundary layer and modify the flow structures on the membrane surface, which improves the filtration flux phenomenon. Numerous authors proposed various designs for developing the filtration execution in membrane tubes (Chen et al., 2014; Chiu and James, 2006;

∗

Ghaffour et al., 2004; Krstic et al., 2006; McDonough et al., 2015; Pal et al., 2008). The majority of these works are based on physical parameters related to the flow structure such as the velocity, wall shear stress, turbulence kinetic energy, dissipation energy and static pressure. Some researchers have interested to the study of mass transfer in a baffled membrane system by means of experiments (Brunold et al., 1989; Finnigan and Howell, 1989; Mackley et al., 1990; Wang et al., 2013). However, and according to the development of data-processing tools and numerical methods during the last decades, the computational fluid dynamic (CFD) is becoming a very suitable device in the membrane science field, where satisfactory results may be obtained with less time and expense of energy (Chen et al., 2013; Liu et al., 2015; Wang et al., 1994). Liu et al. (2009) have studied numerically the effect of central and wall baffles on the performance of a membrane tube. Their results showed that the presence of an array of baffles inside the membrane

Corresponding author. E-mail address: houari [email protected] (H. Ameur). http://dx.doi.org/10.1016/j.cherd.2016.11.005 0263-8762/© 2016 Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved.

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chemical engineering research and design 1 1 7 ( 2 0 1 7 ) 500–508

Nomenclature bt d D Es L l P t u ui uj

Baffle thickness (m) Baffle diameter (m) Tube diameter (m) Eddy size (m) Tube length (m) Distance between two consecutive baffles (m) Pressure (Pa) Time (s) Velocity (m/s) Axial velocity (m/s) Radial velocity (m/s)

Greek letters  Density (kg/m3 ) Dynamic viscosity (Pa s)  ıij Kronecker sign Turbulent viscosity (Pa s) ut

tube cause a frequent change of the flow direction, where the central baffle presents higher shear stresses on the tube wall. Consequently,

Orientation and RO baffle (Case B) for the Right-Orientation, respectively. The baffle thickness (bt ) is 1 mm and its diameter (d) is 12 mm. The distance between two consecutive baffles (l) is equal to 22.5 mm. The first baffle is placed at a distance of 22 mm from the inlet tube. Two methods are suggested for the installation of baffles in the tube: baffles may be mounted on a shaft passing through the center of each baffle, or each baffle may be inserted on small supports fixed on the wall of the membrane tube.

2.2.

The numerical model of Newtonian, incompressible and isothermal fluid, with constant physical properties (water) in a cylindrical tube is described by the continuity and Reynolds averaged Navier–Stokes equations, as follows: ∂ ∂ + (ui ) = 0 ∂t ∂xi

behavior in the zone behind scrapers. Jafarkhani et al. (2012) explored the effects of baffle orientation angles (90◦ and 180◦ ) and diameter ratio (1–3) on the filtration flux. They found that the further extension of the baffle orientation angles from 90◦ to 180◦ enhances considerably the filtration by increasing the fluid average velocity, shear stress and mass transfer on the tube wall. In this paper, turbulent flows in membrane tubes equipped with an array of hemispherical baffles are analyzed with the help of a CFD method. We focus on effects of the baffle orientation on the efficiency of such systems.

2. 2.1.

−

The problem geometry concerns a horizontal tube with inner diameter (D) of 15 mm and length (L) of 200 mm, as illustrated in Fig. 1. Two different orientations of hemispherical baffles are realized, which are: LO baffle (Case A) for the Left-

 ∂

∂p + ∂xi ∂xj

−ui uj





∂uj ∂ui + ∂xj ∂xi

   2 ∂ui −

3



∂xi (2)

requires the modeling of the Reynolds stresses −ui uj in Eq. (2). The Boussinesq hypothesis relates the Reynolds stresses to the mean velocity gradients as seen in the equation below: −ui uj = t

 ∂u

i

∂xi

+

∂ui ∂xi



−

2 3



k + t

∂ui ∂xi

 ıij

(3)

where the turbulent viscosity (t ) is described by:

t = C

k2 , ε

(4)

C = 0.085

The Reynolds number is defined in the hydraulic diameter as: Re = Um Dh /

(5)

For closure of the equations, the RNG k-ε model was used. The RNG k-ε turbulence model is derived from the instantaneous Navier–Stokes equations, using a mathematical technique called “renormalization group” (RNG) methods. This model is very adequate for the prediction of turbulent flows in the membrane tubes (Ahmed et al., 2011; Liu et al., 2009). The turbulent kinetic energy (k) and turbulent dissipation rate (␧) are determined by the following equations: ∂ ∂ ∂ (k) + (kui ) = ∂t ∂xi ∂xj

∂ ∂ ∂ (ε) + (ε ) = ∂t ∂xi ∂xj Fig. 1 – Baffle configurations.

 

The Reynolds-averaged approach to turbulence modeling

Mathematical and numerical solution Problem geometry

(1)

 ∂ui ∂  ∂ + ui uj = ∂t ∂xj ∂xj

the central baffle is the best choice for the filtration execution. In the same framework, Ahmed et al. (2011) and Monfared et al. (2012) confirm that the presence of baffles inside the membrane tubes increases the wall shear stress, which enhances the filtration performances. Rainer et al. (2002) simulated the filtration phenomenon in the presence of rotating discs inside the tubes and reported that the use of bent scrapers yields significant developments in the passing flow and turbulence

Governing equations





t + k

+

 ε

 ∂k ∂xj

 ∂ε ∂xj

+ Pk − ε

(5)

ε2 ε + C1ε ˘ − C∗2ε 

k (6)

502

chemical engineering research and design 1 1 7 ( 2 0 1 7 ) 500–508

where: C∗2ε = C2ε +

C 3 (1 − /0 ) 1 + ˇ3

(7)

Pk is the production term of the turbulent kinetic energy due to the mean velocity gradient. It is defined as: Pk = t S2 . Sis the modulus of mean rate of strain tensor, defined as: 1/2 . S = 2Sij Sij The RNG k-ε turbulence model constants are valued as: C1ε = 1.42,

C2ε = 1.68,

 = Sk/ε

0 = 4.38

ˇ = 0.012.

In order to evaluate the fluid flow behavior through the membrane tube, the permeation phenomenon was investigated. The permeate flux was defined by Darcy’s equation (Jafarkhani et al., 2012) as: j=

TMP  (Rm + Rc )

(8)

where, TMP is the trans-membrane pressure, Rm is the clean membrane resistance. The simulation condition in this study was considered as a single phase; hence the cake resistance (Rc ) was also neglected. Because the membranecompression effect was not considered in this work, the value Rm = 2 × 1010 1/m was used to estimate the flow field (Jafarkhani et al., 2012). For unsteady analyze, we can calculate the permeate flux according to the time filtration, where the time step equal to 0.01 s.

2.3.

Numerical solution

Simulations were achieved with the help of the computer code ANSYS Fluent. Since the model geometry is axial symmetric along the membrane tube centerline and in order to simplify the computational solution, two-dimensional coordinates system was introduced. In industrial membrane systems, the permeate rate is generally less than 0.5% of the total crossflow velocity in the feed tube, thus the wall suction does not influence the fluid flow behavior. In addition, impermeable boundary and no-slip wall conditions are implemented, which is commonly approved in the literature (Ahmed et al., 2011; DaCosta et al., 1994; Koutsou et al., 2004; Liu et al., 2009). For all cases studied in this paper, the inlet average velocity is equal to 0.5 m/s (Re = 7500) and 50 KPa for the outlet pressure. Basing on the Gambit Software, the different computational domains are meshed by triangular grids. The grid independent solution is obtained by comparing the solution for different grid levels. Based on mesh size and the time required for convergence, the adequate grid which is adopted for numerical computations has about 124,000 elements. Fig. 2 presents the generated meshes for the LO baffle case. The governing equations are discretized by a second-order upwind numerical scheme, coupled with the SIMPLE algorithm (Semi-Implicit Pressure Linked Equation) and solved using the finite volume method. The pressure–velocity coupling is performed by using the SIMPLE algorithm. Default under-relaxation factors of the solver are employed. The criterion of convergence is that the normalized residuals which are fixed at 10−7 for the flow equations. Calculation of the numerical domains has required about 14 h of CPU time. The computations were run in Core i5 CPU 2.20 GHz with 6.0 GB of RAM.

Fig. 2 – Triangular mesh for LO baffle case.

3.

Results and discussion

Before the beginning of our investigation, it has been necessary to check the validity of the computer code. For this purpose, we referred to the work of Liu et al. (2009) and we realized the same geometrical configuration. The cross flow micro filtration suspensions of calcium carbonate (7.96 ␮m for the mean particle size) were performed with an inlet velocity equal to 0.5 m/s (Re = 7500) and trans-membrane pressure of 50 KPa. Variations of the permeate flux inside the membrane tube vs. the filtration are presented on Fig. 2 for two values of carbonate calcium and which are 5 g/L (Fig. 3a and c) and 10 g/L (Fig. 3b and d). The comparison is made for unbaffled tubes (Fig. 3a and b) and tubes with wall baffles in a doughnut shape and central baffles in a disc shape (Fig. 3c and d). The comparison between our predicted results and the experimental data of Liu et al. (2009) shows a satisfactory agreement.

3.1.

Flow fields

For the membrane tube without baffles, the formation of the build-up of the boundary layer leads to reduce the filtration flux. This reason has motivated several authors to investigate a number of baffle shapes in order to improve the membrane systems performances (for example, see Cao et al., 2001; Li et al., 1998; Liu et al., 2009). This work examines the changes in flow structures when designing the baffle inside the membrane tube in hemispherical shapes. Fig. 3 shows the flow contours for the inlet velocity 0.5 m/s (Re = 7500). For the membrane tube equipped with RO and LO baffles, the fluid flow is completely turbulent. Accordingly, the fluid particles are more prone to deposit on the membrane walls to form a thick layer, resulting thus in a reduction of the filtration flux. On the other hand, the presence of an array of hemispherical baffles not only increases the flow turbulence, but also it interrupts the appearance of the hydrodynamic boundary layer and it intenses the velocity fluctuations near the tube walls. The integration of LO and RO baffles leads to the diminution of concentration polarization and fouling of membrane, and consequently enhances the performance of such systems (Fig. 4).

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2200

2000

Exp [24]-Without baffles Num [present work]-Without baffles

1600

Permeate flux (L/m .hr)

1800

2

2

Permeate flux (L/m .hr)

2000

Exp [24]-Without baffles Num [Present work]-Without baffles

1800

1600 1400 1200

1400 1200 1000 800

1000 600

0

20

40

60

0

80

20

40

(a)

Num [Present work] - Central baffle Exp (Liu et al., 2009) - Central baffle Num [Present work] - Wall baffle Exp (Liu et al., 2009) - Wall baffle

1800 1600

Permeate flux (L/m .hr)

2

2

Permeate flux (L/m .hr)

1800

80

(b)

Num [Present work] - Central baffle Exp (Liu et al., 2009) - Central baffle Num [Present work] - Wall baffle Exp (Liu et al., 2009) - Wall baffle

2000

60

Filtration time (min)

Filtration time (min)

1600

1400

1200

1400 1200 1000 800

1000 0

20

40

60

80

600 0

Filtration time (min)

20

40

60

80

Filtration time (min)

(c)

(d)

Fig. 3 – Permeate flux vs. filtration time for TMP = 50 KPa, (a) and (c) carbonate calcium = 5 g/L, (b) and (d) carbonate calcium = 10 g/L. Fig. 5 presents the distribution of the velocity fluctuations near to tube wall (0.1 mm away from the wall). It is shown that the hemispherical baffles cause a periodical form of trough and peak value of the wall velocity. The velocity attains its trough value at the middle position between two-consecutive baffles, and then it sharply accelerates and reaches its maximum value at the baffle. After passing the first baffle, the velocity decreases significantly and attains its trough value again. Then, the above phenomena are repeated for the next baffles. When the inlet velocity is equal to 0.5 m/s (Re = 7500), the trough and peak values of wall velocities are about 0.5 and 2.4 m/s, respectively. As a whole, the value of the wall average-velocity is 1.5 m/s, which is greater by about five times compared with that for unbaffled tubes (0.3 m/s). The high values of wall velocities may decrease efficiently the deposition of fluid particles on the membrane surfaces, thereby enhancing the filtration flux. Comparing the RO and LO cases, the intensity of the wall velocity fluctuations remains the same. However, the peak value of the wall velocity is low for the RO case. In similar conditions, the trough and peak values of the wall velocity are about 0.5 and 1.7 m/s, respectively. The value of the wall average-velocity is 1.3 m/s, which is greater by more than four times of that for unbaffled tubes (0.3 m/s).

For the case of the tube without baffles (Fig. 4a), a slight appearance of the hydrodynamic boundary layer is observed near the tube wall causing the pore-feed effect on the membrane surface. The velocity distribution in the tube without baffles (Fig. 4a) is confirmed by several authors (Ahmed et al., 2011, 2012; Liu et al., 2009).

3.2.

Wall shear stress

From the literature, it is known that the intense velocity fluctuation is due to the shear stress on the walls. This proportionality between these two parameters is more required for the design of efficient membrane tubes. Fig. 6 presents the distribution of the wall shear stress along the tubes for unbaffled tubes and tubes equipped with baffles at two orientations: left and right. On the other hand, Figs. 5 and 6 confirm the proportionality indicated previously, hence the tendency of shear stress fluctuation on the wall is similar to that observed in the wall velocity. Consequently, the periodic distribution of peak and trough values of shear stress and velocity at the wall causes a development in mass transfer inside the membrane system (Cao et al., 2001; Li et al., 1998; Liu et al., 2009). For the LO case, the peak and trough values of wall shear stresses are about 85 and 30 Pa, respectively, where the average value is about 43.1 Pa, which is much higher than that for the unbaffled tubes (about 6 Pa).

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Fig. 4 – Contours of velocity magnitude along the tube, (a) empty tube, (b) LO baffle, (c) RO baffle. 2.5

LO Baffle

RO Baffle

Without baffle

LO baffle

RO baffle

Without baffle

100

Wall shear stress (Pa)

Wall velocity (m/s)

2.0

1.5

1.0

0.5

80

60

40

20

0.0 0.00

0.05

0.10

0.15

0.20

Position (m)

Fig. 5 – Velocity distributions on the tube wall.

0 0.00

0.05

0.10

0.15

0.20

Position (m)

Fig. 6 – Shear stress distributions on the tube wall.

For the RO case, the average value of wall shear stresses is 40 Pa. Compared with the unbaffled tube, the increases of the average values of wall shears are about 5.5 and 5 time for the LO and RO cases, respectively. Therefore, the LO baffle is the best choice for obtaining the highly filtration performance, since the higher values of wall shear stresses can improve significantly the mass transfer in membrane tubes (Zydney and Colton, 1986).

3.3.

Stream function

Fig. 7 presents the spatial distribution of the stream function along the tubes. For the membrane without baffles, the streamlines are parallel to all other baffle cases throughout the

Fig. 7 – Stream function distributions along the tube, a) tube without baffle, b) LO baffle, c) RO baffle.

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chemical engineering research and design 1 1 7 ( 2 0 1 7 ) 500–508

75

LO Baffle RO Baffle Without baffle

0.4

LO Baffle RO baffle Without baffle

70

Static pressure (KPa)

2

2

Turbulence kinetic energy (m /s )

0.5

0.3

0.2

0.1

0.0

65

60

55

50

0.00

0.05

0.10

0.15

0.20

0.00

0.05

Position (m)

2

3

Turbulent dissipation rate (m /s )

LO Baffle RO Baffle Without baffle

1400

0.15

0.20

1200 1000 800 600

Fig. 10 – Distribution of the static pressure along the tubes. 8 mm

100

Wall shear stress (Pa)

Fig. 8 – Distribution of the turbulence kinetic energy along the tube wall. 1600

0.10

Position (m)

400

10 mm

12 mm

80

60

40

20

200

0 0.00

0 0.00

0.05

0.10

0.15

0.05

0.10

0.15

0.20

Position (m)

0.20

Position (m)

Fig. 9 – Distribution of the turbulent dissipation rate along the tube wall.

Fig. 11 – Effect of the baffle size on the wall shear stress, for the LO case.

3.5. tube length. On the other hand, there is a significant change of the flow structures for the baffled tubes (LO and RO baffles). The local stream function is obviously appearing around baffles and tube walls. These lines tend to twist outward toward the wall-bordering region. Two eddies are formed behind the baffle for each case. The size of these eddies (Es /l) is 0.5 and 0.9 for the RO and LO cases, respectively. The formation of eddies behind baffles perturb the boundary layer in this region, also it can sweep the particles deposited on the membrane surface (Brunold et al., 1989). The LO configuration is found again to be more efficient that the RO case.

3.4.

Turbulent characteristics

Effects of the baffle orientations on the distribution of turbulent kinetic energy and energy dissipation rates are illustrated in Figs. 8 and 9, respectively. Compared with the unbaffled tube, the baffled membrane systems generate higher turbulence kinetic energy, which means that the fluid flow in the baffled tubes is entirely turbulent. This increase of turbulent kinetic energy can disturb the formation of the hydrodynamic boundary layer and reduces the deposit of fluid particles on the membrane walls. However and at the same time, the increase of the turbulent kinetic energy generates high values of the local energy dissipation, which increases the pressure drop in the membrane system.

Static pressure

Distribution of the static pressure along the tube is presented for three cases, as shown in Fig. 10. For an inlet velocity equal to 0.5 m/s (Re = 7500), the pressure drop along the channels is approximately 23 and 19.5 KPa for the LO and RO cases, respectively, which is much higher than that for the tube without baffles. The high-pressure drop leads to the increase in additional energy cost of the membrane tube. There are two main reasons for the increase of the pressure drop inside the baffled system. First, the presence of an array of hemispherical baffles (LO and RO baffles) causes a frequent change in the flow direction and intense velocity fluctuation, which can increase the frictional loss of the fluid flow. Secondly, the eddy formed behind baffles also results in the increase of energy loss due to the turbulent energy dissipation.

3.6.

Performance evaluation of the LO configuration

There are two important geometrical parameters that influence directly the execution of the filtration flux in a membrane tube: the baffle size (diameter, d) and the space between two successive baffles (l), because they significantly influence the distribution of wall shear stresses and the pressure drop along the tube. For the LO case and in order to evaluate the effect of baffle size, three geometries are realized and which are: d = 8, 10 and 12 mm, respectively. The length l is fixed at 22.5 mm. Fig. 11 illustrates clearly the effect of baffle size on the wall shear

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chemical engineering research and design 1 1 7 ( 2 0 1 7 ) 500–508

Wall shear stress (Pa)

20

Pressure drop (KPa)

l = 12 mm l = 16 mm l = 22.5 mm

100

15

10

5

80

60

40

20 0

8

10

0 0.00

12

Baffle size (mm)

0.15

0.20

Fig. 13 – Effect of the baffle spacing (l) on the wall shear stress, for the LO case.

stress. The raise of the baffle size increases the value of wall shear stresses. The average values of wall shear stresses are about 12.6, 21 and 43.1 Pa, when the baffle sizes are 8, 10 and 12 mm, respectively. Therefore, to obtain a better filtration performance, the LO baffle with 12 mm of size is recommended. However, the increases in the baffle size yields more pressure drop, as noticed in Fig. 12. Fig. 13 presents the effect of the length l on the wall shear stresses. As observed, the length l clearly influences the wall shear stress, since it determines the required number of baffles when the length of membrane tube is constant. For the tube length of 200 mm and when the baffle clearances are 12, 16 and 22.5 mm, the required numbers of baffle are 15, 11 and 8 with the corresponding values of wall shear stresses 49.8, 46.3 and 43.1 Pa, respectively. It is evident that the average value of wall shear stress decreased with the increment of baffle clearance, as observed in Fig. 14.

Pressure drop (KPa)

25

20

15

10

5

0

12

16

22.5

Position (m) Fig. 14 – Effect of the baffle spacing (l) on the pressure drop, for the LO case.

Validation and supplementary comparison 0.5 m/s, the trans-membrane pressure is 50 KPa and the baffle spacing (l) is 22.5 mm. Analysis of results given on this figure reveal that the hemispherical baffles generate a high steady state flux than the

Variations of the permeate flux vs. the filtration time are presented in Fig. 15 for two values of the carbonate calcium suspensions (5 and 10 g/L). The inlet velocity is equal to Without baffles Wall baffle (doughnut shape) Central baffle (disc shape) RO baffle LO baffle

2000

1600 2

2

1600

1400

1200

Without baffles Wall baffle (doughnut shape) Central baffle (disc shape) RO baffle LO baffle

1800

Permeate flux (L/m .hr)

1800 Permeate flux (L/m .hr)

0.10

Position (m)

Fig. 12 – Effect of the baffle size on the pressure drop, for the LO case.

3.7.

0.05

1400 1200 1000 800

1000 0

20

40 Filtration time (min)

(a)

60

80

600 0

20

40 Filtration time (min)

60

(b)

Fig. 15 – Effect of the baffle orientation on filtration, for TMP = 50 KPa, (a) carbonate calcium = 5 g/L, (b) carbonate calcium = 10 g/L.

80

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Table 1 – Summary of major numerical works on baffled membrane tubes having different baffle shapes on the filtration execution. Authors

Liu et al. (2009)

Ahmed et al. (2011)

Jafarkhani et al. (2012)

Ahmed et al. (2012)

Present work

Baffle shapes

Size/baffles spacing (mm)

Wall baffle Central baffle

12/22.5 12/22.5

TMP = 50 KPa, calcium carbonate 5 g/L 10 g/L 36% 52% 53% 89%

Wall baffle Rod baffle

TMP = 50 KPa, TiO2 = 1 g/L 12/22 12/22

20% 50%

Filtration time (min)

90

120

Semi circular baffle with baffle orientation angle: 90◦ 180◦

15 of diameter tube/22.5 15 of diameter tube/22.5

16% 29%

Conical baffles: LO baffle RO baffle

12/20 12/20

TMP = 50 KPa, TiO2 = 1 g/L 55% 61%

Calcium carbonate, 5 g/L, TMP = 50 KPa 90

Hemispherical baffles: RO baffle LO baffle

120

Calcium carbonate, TMP = 50 KPa

12/22.5 12/22.5

membrane without baffles, with an increase by 64% (LO baffle) and 57% (RO baffle) at the feed concentration of 5 g/L. When the feed concentration is 10 g/L, the flux enhancement is much higher, reaching 96% for the LO baffle and 85% for the RO baffle, respectively. In addition, at the same feed concentrations, the LO baffle achieves higher flux than that of the RO baffle, with an increase by 7% (C = 5 g/L) and 11% (C = 10 g/L), respectively. Also from Fig. 15, the LO baffle gives a better enhancement than the baffle shape suggested by Liu et al. (2009) (as validated on Fig. 3). When the feed concentration is 5 g/L, the LO baffle gives an enhancement by about 18% and 7% compared with the wall and central baffles, respectively. For the feed concentration of 10 g/L, the enhancements obtained by the LO baffle are about 21% and 7%, compared with the wall and central baffles, respectively. Table 1 shows a comparison between the present results and other works available in literature. This comparison confirm that the LO baffle achieves the best rate of filtration flux.

4.

Permeate flux optimization (comparison with smoothed membrane tube)

Conclusion

A numerical investigation was carried out to evaluate the qualitative and quantitative performances of hemispherical baffles in a membrane tube. The velocity, shear stresses at the wall, turbulence characteristics and the static pressure are predicted for three geometrical configurations: a membrane tube without baffle, a membrane tube with RO baffles and other with LO baffles. The shearing force is the parameter used to estimate the filtration flux and the deposit of the fluid particles on the membrane surface. The obtained results showed that the presence of an array of hemispherical baffles in the membrane tube intensifies the local wall velocity fluctuations and the wall shear stress, which is important to enhance the filtration flux by minimizing the deposition of particles on the membrane surface. The LO baffle case produces the highest values of wall

5 g/L 57% 64%

10 g/L 85% 96%

80

shear stresses and gives the best filtration flux rate compared with tube without baffles and others baffled tubes available in the literature. In conclusion, the presence of an array of baffles on the wall of membrane causes strong changes in the flow direction and generates eddies behind the baffles, which increases the pressure drop and the energy cost due to the energy dissipation of the turbulent flow. Therefore, it is easy to increase the filtration flux in a membrane tube. However, for future works, the challenging task is the diminution of the pressure loss penalty during local mass transfer in membrane installations.

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