DESALINATION

ELSEVIER Desalination 146 (2002) 195-201 www.eisevier.com/locate/desal

A CFD study of unsteady flow in narrow spacer-filled channels for spiral-wound membrane modules

J. Schwinge”, D.E. Wiley”“, D.F. Fletcherb “UNESCO Centre for Membrane Science and Technology, School of Chemical Engineering and Industrial Chemistry,

The University of New South Wales, Sydney, NSW 2052, Australia Tel. +61 (2) 9385-4304; Fax +61 (2) 9385-5966; email: D. Wiley@unsw.edu.au

bDepartment of Chemical Engineering, The University of Sydney, Sydney, NSW 2006, Australia

Received 7 February 2002; accepted 21 February 2002

Abstract

In spiral-wound membrane modules, spacers are used to enhance wall shear stress and to promote eddy mixing, thereby reducing wall concentration and fouling. Insights into the effect of spacer filaments on flow patterns in narrow channels were obtained using a computational fluid dynamics (CFD) code. The flow patterns were visualized for different filament configurations incorporating variations in mesh length, filament diameter and for channel Reynolds numbers up to 1000. The simulated flow patterns revealed the dependence of the formation of recirculation regions on the filament configuration, mesh length, filament diameter and the Reynolds number. When the channel Reynolds number is increased above 300, the flow becomes super-critical showing time-dependent movements for a filament located in the center of a narrow channel; and when the channel Reynolds number is increased above 500, the flow becomes super-critical for a filament adjacent to the membrane wall. For multiple filament configurations, flow transition can occur at channel Reynolds numbers as low as 80 for the submerged spacer at a very small mesh length (l,,,/hch = 1) and at a slightly larger Reynolds number at a larger mesh length (l,,/h=,, = 4). The transition occurs above Rech of 300 for the cavity spacer (ln/hd, = 4) and above Re, of 400 for the zigzag spacer (l,,/hch = 4).

Keywords: Feed spacer; Computational fluid dynamics (CFD); Unsteady fluid flow; Spiral-wound membrane module

1. Introduction major problem for membrane applications is

Treatment of water and other process fluids with membranes are growing applications. A

*Corresponding author.

concentration polarization which reduces the flux and which also can induce fouling. According to the boundary layer theory [l], an increase in velocity reduces concentration polarization due

Presented at the International Congress on Membranes and Membrane Processes (ICOM), Toulouse, France, July 7-12, 2002.

001 l-9164/02/$- See front matter 0 2002 Elsevier Science B.V. All rights reserved PII: SO0 1 I-9 164(02)00470-8

196 J. Schwinge et al. /Desalination 146 (2002) 195-201

to a higher wall shear stress as velocity increases, but the changes in hydrodynamic conditions in spiral-wound modules are limited by module telescoping. Therefore, net-type spacers are used in spiral-wound modules to enhance mass trans- fer and to reduce concentration polarization and to maintain the channel height.

Many researchers have examined flow around cylinders placed in the middle of a wide “free- flow” channel where interactions with the chan- nel walls are neglected. They found that for cylinder Reynolds numbers above 40, the recirculation region starts to show periodic movements. For a cylinder Reynolds number greater than 200, the flow is found to be unsteady and a vortex street develops behind the cylinder

[21* For flow in narrow empty channels, the flow

is laminar for Reynolds numbers up to 2000 [ 11. However, the flow in narrow obstructed channels becomes unsteady at much smaller Reynolds numbers. The flow can become unsteady and show periodic movements for Reynolds numbers as low as 200, depending on the geometry of the obstructions [3,6]. Flow over a backward-facing rectangular step is stable for much higher Rey- nolds number than for other obstacles submerged in the channel, the flow being time independent for Reynolds numbers as high as 2500 [7]. However, small disturbances in the upstream region propagate unsteadiness downstream.

In this paper we examined the sub- and super- critical flow patterns in narrow two-dimensional channels for single and multiple filaments. As the paper focused on cylindrical spacer filaments orientated transverse to the main flow direction, two-dimensional CFD simulations were used. These two-dimensional calculations are an excel- lent screening device for future evaluations of more complex spacer geometries and allow the effect of numerical parameters and modeling assumptions to be studied for situations in which grid independence can be guaranteed.

2. Numerical modeling procedure

The fluid used is water at a temperature of 293 K which is assumed to be incompressible, isothermal and to have constant fluid properties. The fluid motion is described by the Navier- Stokes equations. The governing Navier-Stokes equations are valid for all Reynolds numbers, but under laminar conditions they can be solved without the need to consider the resolution of turbulent eddies [2,8]. These equations were solved using a CFD code (CFX4, Version 4.3, AEA Technology). A small enough grid size was chosen, based on the comparison of results from a succession of finer meshes, to ensure that the results were independent of the grid.

Five filament configurations were examined: (1) a single cylindrical filament adjacent to a membrane wall, (2) a single cylindrical filament placed in the center of a membrane channel, (3) a cavity spacer with multiple cylindrical filaments adjacent to one membrane wall, (4) a zigzag spacer with multiple cylindrical filaments located alternately adjacent to the top and bottom mem- brane wall, and (5) a submerged spacer with multiple cylindrical filaments placed in the center of a membrane channel [9, lo].

3. Flow patterns in narrow and obstructed two dimensional channels

3.1. Flow projiles for sub-critical Reynolds numbers in the channel

Fig. 1 shows steady flows at sub-critical Rey- nolds numbers for a section of the flow channel in the region of the spacer filament for the five filament configurations.

For a single filament adjacent to the bottom wall, a small recirculation region is formed in front of the filament and a much larger recircu- lation region is formed behind the filament. The size and length of the recirculation region increases with Reynolds number. Similarly, for a single filament located in the center of the

Single filament adjacent to the wall

Single filament centered in the channel

Cavity spacer

Zigzag spacer

Fig. 1. Steady flow distributions along the channel for five filament configurations at Re, equal to 100 (d/h, = 0.5, I,,/h,

= 4 for multiple filament configuratiks).

channel, a large recirculation region is formed behind the filament and the size and length of the recirculation region increases with Reynolds number.

At very small Reynolds numbers or large mesh lengths [9,10], the multiple filament cavity and the submerged spacers produce large recirculation regions behind each filament similar to the regions formed for single filaments. However, with an increase in Reynolds number or decrease in mesh length, the recirculation regions in front of and behind sequential filaments influence each other and merge to form one large recirculation region between filaments.

In contrast, the multiple filament zigzag spacer forces the channel flow into a zigzag pattern. The recirculation regions behind each filament are forced to reattach to the membrane wall by the consecutive filament at the opposite membrane wall. Only at very small mesh lengths does the separation streamline of the recircu-

lation region detach from the membrane wall forming one large recirculation region between sequential filaments at the same membrane wall. However, such very small mesh lengths are impractical in spiral-wound modules because the spacer filaments would cover a high amount of membrane area, significantly reducing the flux [9,101.

3.2. Flow patterns for super-critical Reynolds numbers

Practical application of spiral-wound modules often requires flow rates which exceed sub- critical Reynolds numbers, leading to transient flow conditions in the feed channel. To check our method of modeling, transient flows were first simulated for the flow in a “free flow” channel using a single cylinder with the same diameter as the spacers simulated earlier. The flow channel was wide enough to avoid any effects of the walls

198 J Schwinge et al. /Desalination 146 (2002) 195-201

on the flow around the cylinder and long enough to avoid any interference of the channel entrance and exit on the formation of vortices behind the filament.

Our simulations of the single cylinder in a “free flow” channel agree with accepted litera- ture findings reported earlier [2]. A vortex street is formed for Re, greater than 200. In addition, the shedding frequency obtained here of 139 Hz shows good agreement with a value of 143 Hz predicted by Strouhal equation [2]:

- - 0.198. l-19.7 f?f_

urn ( I %yt (1)

The cylinder Reynolds number is defined by:

(2)

Having validated our method of modeling transient flows, we then modeled flow in narrow spacer-filled channels at super-critical Reynolds numbers. To characterize the flow, a modified channel Reynolds number Re, was used which accounts for changes in the superficial velocity uc,, and hydraulic diameter dh due to the presence

of spacer filaments [9]:

In the transient mode, the filament Reynolds number was varied from 38 to 1000. Time steps of 5 us were used and convergence was achieved within a maximum of 20 interations for each step. For a single filament located in the center of the narrow channel, the flow does not show any transient movements for Re, below 200 despite using small time steps and a fine mesh. Fig. 2 shows the transition to unsteadiness that occurs

above Re, = 300. At the Reynolds number where the transition begins the recirculation region just begins to flap behind the filament, but with an increase in Reynolds number, the time dependent movements increase and convect downstream indicating a “full” transition to unsteady flow.

For a single filament adjacent to the bottom wall, the flow is steady for Re, below 600. Above Rech = 600, small disturbances caused by the flow recirculation propagate unsteadiness downstream, as shown in Fig. 3. Despite the different flow profile of the obstruction used here, it is interesting that our value for the transi- tion to unsteadiness agrees with the findings of Kaiktsis et al. [7] for flow over a backward- facing step.

Comparison of the transient results suggests that the walls near a cylinder damp the transition to unsteadiness. In addition, location of a cylinder at a wall further stabilizes the flow.

Fig. 4 shows the flow pattern for multiple filaments located in the center of the channel at a mesh length of Z,,/h,,, = 1 and at Re, = 195. A

Fig. 2 Unsteady flow caused by a single filament located in the center of the obstructed and narrow channel (d,/h, = 0.5) at Re,, equal to 500.

J. Schwinge et al. /Desalination 146 (2002) 195-201 199

large and “fully formed” but unsteady recircu-

lation region exits between sequential filaments. The recirculation regions show periodic move- ments at a frequency identical to that for a single filament in the center of the channel.

For the submerged spacer at Z,,/hch = 4, as shown in Fig. 5, large eddy movements exist between sequential filaments for Re, = 360. However, the flow becomes transient at Rech

above 200 which is similar to the value for transition to unsteadiness for a single filament located in the center of the channel. In addition, a small disturbance caused by an upstream filament causes an increase in the amplitude of

flow movements for consecutive filaments. For the cavity spacer at Z,,/hc,, = 4, the flow

becomes transient at Rech above 300 which is a lower Re, than for transition to unsteadiness for

. _ .I \ d * .,.- 1 “_.. “._ _ - .,

I

I /

/ _o,oo2 i .,. ,..,.., .._. . .“.“.. ...” .._. “. 150 200 120 220

time [ms]

time [ms]

Fig, 3. Unsteady flow for Re,,, equal to 1000 when a filament is adjacent to the wall and small flow disturbances are convected downstream (d//h, = 0.5).

40 60 80

lime [ma]

Fig. 4. Periodic movement of the recirculation region between sequential filament for a spacer with filaments located in the center of the channel at a small mesh length, 1,/h=,, = 1 and Re, = 195 (d/h, = 0.5).

200 J. Schwinge et al. /Desalination I46 (2002) 195-201

Fig. 5. Propagation of large eddy movements between sequential filaments located in the center of the channel at a large mesh length, l,Jh, = 4, and Re, = 360 (d,/h, = 0.5).

Fig. 6. Propagation of large eddy movements between sequential cavity spacer filaments caused by small upstream disturbances at Re, = 718 (d//h, = 0.5).

Fig. 7. Propagation of large eddy movements behind zigzag spacer filaments caused by small upstream disturbances at Re, = 718 (d//h, = 0.5).

a single filament adjacent to the wall. For a higher Reynolds number, a “fully formed” recir- culation region appears between the first two sequential filaments, but further downstream, as

shown in Fig. 6, the unsteady flow breaks the “fully formed” recirculation region and eddies move along between sequential filaments.

Fig. 7 shows the unsteady recirculation

J. Schwinge et al. /Desalination 146 (2002) 195-201 201

regions that exist at Re, above 400 for the zigzag spacer at Z,,/h, = 4. The transition to unsteadiness for the zigzag spacer occurs at a smaller Re, than for a single filament adjacent to the wall but at a larger Re, than for a cavity spacer.

4. Conclusions

Computational fluid dynamics calculations reveal complex relationships between filament configurations, mesh length, filament diameter, Reynolds number and the formation of recircu- lation regions. The transition to time-dependent flows in an obstructed channel occurs at much smaller Reynolds numbers than in an empty narrow channel. For a single filament in a narrow channel the wall damps the transition which occurs at slightly higher Reynolds numbers than for a cylinder in a “free flow” channel. Different stages are observed for the transition to unsteadi- ness from slight movement to downstream convection of recirculation regions.

Accurate evaluation of the two-dimensional time-dependent flows demands extremely fine numerical grids and small time steps which increases the computational costs. Coarse grids and large time steps suppress the development of the time-dependent flow movements.

The complexity ofthe two-dimensional results suggest that extension of the calculations to three dimensions will require careful and systematic identification of appropriate modeling proce- dures. Time-dependent movements of three- dimensional recirculation regions are likely to be extremely complex and sensitive to small changes in modeling conditions.

5. Symbols

df -

> L

h -

lLh -

Filament diameter, m Hydraulic diameter, m Shedding frequency, Hz Channel height, m Mesh length, m

Recy, - Rech - 24 -

24 - ch

~co -

v -

Cylinder Reynolds number Channel Reynolds number Velocity, m/s Superficial velocity in the spacer filled channel, m/s Velocity at an infinite distance from the filament, m/s Kinematic viscosity, m%

References

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CFX 4.3 User Manual, CFX International, AEA Technology, Harwell, Didcot, Oxfordshire, UK. J. Schwinge, D.E. Wiley and D.F. Fletcher, Simula- tion of the flow around spacer filaments in a small channel. Part I: Hydrodynamics. Ind. Eng. Chem. Res., in press. J. Schwinge, D.E. Wiley and A.G. Fane, Flux improvements with a novel spacer design for ultra- filtration. Proc. 6th World Congress of Chemical Engineering, Melbourne, Australia, 2001.