A c r s m filter.pdf

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Journal of Membrane Science 165 (2000) 1929

A comparison of rotating and stationary membrane disk lters usingcomputational uid dynamicsChristophe A. Serra , Mark R. Wiesner

Rice University, Department of Environmental Science and Engineering, 6100 Main Street, Houston, TX 77005, USA

Received 28 July 1998; received in revised form 21 June 1999; accepted 22 June 1999

Abstract

Rotating disk lters, implemented either with an impermeable disk rotating above a stationary membrane disk or witha stationary bafe next to a rotating membrane disk, are investigated numerically using a commercial computational uiddynamics package. The uid is assumed to be Newtonian, incompressible, non-fouling and isothermal. The model isused to describe turbulent ow in the vessel surrounding the rotating disk.

For givenvalues ofthe ow rate andRPM,stationary membrane disk ltersrequire less powerinput.Rotatingmembranedisk lters produce a higher shear stress on the membrane surface which may reduce fouling but may also result in a reversed owof permeate due to the back pressure induced by centrifugal force on uid within the membrane disk. Operating conditionsanddesignparameters shouldbe selected to minimize this back pressure phenomenon and maximize the effective membraneavailable for ltration. 2000 Elsevier Science B.V. All rights reserved.

Keywords: Stationary membrane disk; Rotating membrane disk; Computational uid dynamics; Turbulent ow; Filter design

1. Introduction

Membrane ltration often relies on the presence of ashear stress at the membrane surface to reduce the ac-cumulation of foulants [1,2]. In the classicalcross-owltration, the shear stress is brought by the tangentialow along the membrane surface but as a result leadsto pressure drops. For high concentrated suspensions,the shear stress to reduce fouling may be so high thatthe required ow rate would induce an unacceptablepressure drop . For rotating disk lters, the shear stress

Corresponding author. Present address: Ecole de Chimie,

Polym eres et Mat eriaux, D epartement Polym eres, 25rue Becquerel, 67087 Strasbourg Cedex 2, France; Tel.:+ 33-388-13-69-25; fax: + 33-388-13-69-23. E-mail address: [email protected] (C.A. Serra).

and ow rate are unlinked since shear stress is only

a function of the rotational speed. Therefore, theselters appear to be most applicable to the clarica-tion of very high concentration suspensions [34] andthe separation of biological products [56]. Commer-cially, rotating disk lters have been implemented bothas membrane disks rotating between stationary bafes[7], and as xed membrane disks next to rotating baf-es [8]. The hydrodynamics of these membrane ltersare expected to be greatly affected by any variation inoperating conditions (ow rate, RPM) and geometryparameters (disk radius, clearance between membraneand bafe). However, there are few guidelines in theliterature for the design of such lters.

This work deals with the use of computational uiddynamics (CFD) to investigate and compare the per-formance of rotating membrane disk lters (RMDFs)

0376-7388/00/$ see front matter 2000 Elsevier Science B.V. All rights reserved.PII: S0 376-7388 (99)0021 9-7


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20 C.A. Serra, M.R. Wiesner/ Journal of Membrane Science 165 (2000) 1929

Fig. 1. View of the membrane disks.

and stationary membrane disk lters (SMDFs) over arange of operating conditions and design parameters.

2. Methodology

2.1. Filter units

In the case of the RMDF, the membrane disk ismounted on a rotating shaft via two retaining sleevesand washers. The stationary membrane disk in theSMDF conguration is mounted to the exterior wallof the vessel. The membrane disk is a porous mediumwith a at microltration membrane on each of itsfaces (Fig. 1). For the purpose of symmetry, the feed

inlet is assumed to be a slit around the vessel oppositeto the rotating disk tip. In the RMDF conguration, theuid ows through the membrane to the center whereit exists through the hollow shaft. In the SMDF con-guration, the permeate is collected at the peripheryof the vessel. Both lters operate in dead-end mode.Parameter baseline values were selected to correspondto those anticipated in the laboratory and full scaleunits (see Table 1).

2.2. Computational uid dynamics

A commercial CFD package, FIDAP (Fluid Dy-namics International, Evanston, IL, USA), was used tomodel the hydrodynamics of those two rotating disk lters. Turbulence, which occurs in such geometries

Table 1Parameter baseline values

Parameter Value

Tank radius 7.5 10 2 mShaft radius 1.3 10 2 mClearance between disks 7.14 10 2 mMembrane permeability 6.5 10 16 m2

Membrane thickness 10 4

mSupport permeability 8.18 10 12 m2

Support thickness 3.5 10 3 mBafe permeability NoneBafe thickness 3.6 10 3 mRotating disk radius 7.1 10 2 mGap with cylindrical wall 4 10 3 mRetaining seal length 10 2 mWasher length 1.2 10 2 mStationary disk radius 7.5 10 2 mGap with rotating shaft 4 10 3 mRetaining seal length 3.33 10 3 mFiltration ux 200 l h 1 m 2

especially at high rotational speeds, is typically mod-eled by either the zero-equation model based on thePrandtl mixing length or the model. The CFDtool accommodates ow through porous media usingthe ForchheimerBrinkman model [9]. The uid owequations are solved by the nite element method.

Symmetry in lter units allows the simulation do-main to be reduced to a quadrant of a cut throughthe vessel modeled in two dimensions (Fig. 2). Thereduction in the computational domain greatly facili-tates modeling under turbulent conditions. The radialaxis is along the stationary disk while the axial axisruns along the shaft.

In this work, the uid is assumed to be Newto-nian, isothermal and incompressible. Furthermore,steady-state solutions are calculated assuming con-stant membrane permeability. Thus, membrane foul-ing is not considered. No-slip boundary conditionsare set at all solid wall boundaries (cylindrical wall,rotating shaft, washer, retaining seal and bafe). Theazimuthal velocity ( v ) on the rotating disk and shaftsurface is set according to the equation:

v = r (1)

where r is the radial distance and the rotationalspeed. Flow in the inlet and outlet regions is assumedto be uniform. The model is used to describeturbulent ow within the vessel and has been found


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C.A. Serra, M.R. Wiesner/ Journal of Membrane Science 165 (2000) 1929 21

Fig. 2. Computational domain.

to yield a satisfactory representation of ow in similargeometries [1011].

2.3. Simulations

The global transmembrane pressure ( pG) is de-ned as the difference between the inlet pressure andthe permeate exit pressure (Fig. 2) and is related tothe power consumption ( P ) required to drive the uidthrough the lters:

P = Q 0 p G (2)

where Q0 is the overall throughput ow rate. Thepower consumption to rotate the shafts is not consid-ered in this study since the lters are compared for thesame rotational speed.

The pressure on the feed side of the membrane sur-face and that on the permeate side are calculated asa function of the radial position. The difference of those two pressures is dened as the local transmem-brane pressure ( pL). Knowing this pressure differ-ence along the membrane, one can evaluate the di-mensionless cumulative ow rate ( Q*) as the perme-ate ow rate through the membrane from the edge of the washer (RMDF) or retaining seal tip (SMDF) to

a radial distance r over the overall throughput owrate (Q0):

Q (r) = rr0 2(L p/e)r p L (r) dr

Q 0(3)

where r 0 is the radial position of the washer edge orretaining seal tip, e the membrane thickness, Lp themembrane permeability and the permeate viscosity.Increases in the dimensionless cumulative ow ratewith r indicate that increments in membrane area by

increasing disk radius produce additional ow.The code used in this study has been validated byEngler [12] by comparing the global transmembranepressures returned by simulations and those obtainedfrom experiments to achieve a specic ux. The dis-crepancy was found to be less than 7% so that the codecould be considered accurate enough to be used as anassessment tool.

3. Results and discussion

3.1. Flow pattern within the lters

Under the inuence of disk rotation, the uidmoves radially outward along the rotating disk and


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Fig. 3. Variation of the radial velocity across the lters as a function of the RPM at a radial distance of 4.3 10 2

m for RMDF and6.26 10 2 m for SMDF (: SMDF; - - - -: RMDF).

returns inward in the vicinity of the stationary disk (Fig. 3). Variations in the azimuthal velocity indicatethat the boundary layers on the stationary and rotat-ing disks remain close to those surfaces leading to a

Fig. 4. Variation of the azimuthal velocity across the lters as a function of the RPM at a radial distance of 4.3 10 2 m for RMDF and6.26 10 2 m for SMDF (: SMDF; - - - -: RMDF).

core uid which rotates nearly as a solid body with arotational speed smaller than that of the rotating disk (Fig. 4). The uid entering the vessel ows along thecylindrical wall towards the stationary disk where it


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Fig. 5. Streamlines and subsequent values of the stream function at 1500 RPM for the SMDF (top) and RMDF (bottom).

moves radially to the shaft. The uid then returns ax-ially towards the rotating disk to compensate the uidthrown radially away by centrifugal force as shownin Fig. 5. The streamline contour represents basicallythe curves (streamlines) traced out by a uid element.

Each curve is actually a line of iso-stream functionfrom which the direction of the ow can be deduced[13]. A zone of internal circulation with a high veloc-

ity appears in the upper portion of the chamber closeto the membrane surface. This recirculation ow pat-tern has been previously described by Daily and Nece[14] and more recently by Rudniak and Wronski [15]in the case of non-porous disks. Due to the relatively

small permeability, characteristic of membrane ltra-tion, the overall ow pattern is dominated by disk rotation.


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Fig. 6. Variation of the dimensionless cumulative ow rate along the membrane as a function of the RPM (: SMDF; - - - -: RMDF).

3.2. Effect of the rotational speed on membrane performance

The membrane performance expressed as the vari-ation of the dimensionless cumulative ow rate withrespect to the radial position is shown for each l-

ter in Fig. 6. As expected, the dimensionless cumula-tive ow rate increases along the membrane. However,while the SMDF is scarcely affected by any variationin the RPM, the RMDF exhibits strong deviations.Hence, for the higher RPM, the dimensionless cumu-lative ow rate passes through a maximum. A portionof the membrane is submitted to a reversed ow withsome of the permeate returning to the feed compart-ment due to a reversal in the sign of transmembranepressure. In the permeate compartment, the pressurereects a balance between pressure loss through thedisk medium and membrane and the centrifugal forceeffects. The centrifugal force ( f v) due to disk rotationacting on the uid inside the support is proportionalto the square of the rotational speed and the radialposition:

f v = r 2 (4)

where is permeate density. Therefore, at large radialpositions and high rotational speeds, the centrifugalforce effects are higher than the pressure loss effectsresulting in local permeate pressure which is higher

than the feed side pressure and in a negative localtransmembrane pressure. In addition to reducing theeffectiveness of installed membrane area, this back pressure phenomenon might also damage the mem-brane over time since forces acting in an opposite di-rection could potentially tear the membrane from itssupport.

Pressure on the permeate side increases due tocentrifugal force effects requiring a higher globaltransmembrane pressure to drive the same amount of uid across the membrane and through the poroussupport. Therefore, the RMDF exhibits a higherglobal transmembrane pressure and is more affectedby variations in RPM (Fig. 7). For instance, at 1500RPM, the SMDF is calculated to have a global trans-membrane pressure which is 68% less than that in


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Fig. 7. Global transmembrane pressure as a function of the RPM. Percentages give the reduction for SMDF in comparison with RMDF.

the RMDF. As a result, power consumption is ex-

pected to be smaller when the membrane disk isxed.

However, as shown in Fig. 8, shear stresses on thesurface of the SMDF membrane are signicantly lessand more uniform than those on the RMDF mem-brane. On the rotating membrane disk, the shear stressvaries linearly with respect to the radial position and

Fig. 8. Variation of the shear stress along the membrane as a function of the RPM (: SMDF; - - - -: RMDF).

increases with the RPM. The shear stress is imposed

by the azimuthal velocity gradient across the bound-ary layer which is a function of radial position androtational speed [16]. A higher shear stress may re-duce fouling leading to a lower global transmembranepressure over time [1,2,4].

The remaining results presented here assume arotational speed of 1500 RPM.


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Fig. 9. Variation of the dimensionless cumulative ow rate along the membrane as a function of ltration ux (: SMDF; - - - -: RMDF).

3.3. Reducing the back pressure

Increases in ltration ux reduce the effects of alocal back pressure at the membrane disk extremity(Fig. 9). Increasing the ltration ux leads to an in-

Fig. 10. Variation of ltration ux as a function of the global transmembrane pressure for the RMDF.

creased feed side pressure. Pressure loss through thedisk support also increases. However, the centrifugalforce is only a function of r and (see Eq. (4)). There-fore, there is a value of the ltration ux for whichthe back pressure effect is overwhelmed. As dictated


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by Darcys law, the ltration ux varies linearly as afunction of the global transmembrane pressure (Fig.10). Yet, one can remark that, except for the case of no rotation, those lines do not pass through the origin.The x-intercept is a measure of the global back pres-sure ( pbck ) which must be overcome to initiate the l-tration. As previously discussed, global back pressureincreases with RPM. For example, global back pres-sures of 1.7, 10 and 26.4 kPa were calculated at RPMsof 375, 900 and 1500, respectively yielding the fol-lowing correlation between global back pressure andthe square of the rotational speed ( R2 = 0.99).

p bck = 1.18 2 (5)

The back pressure can also be reduced by decreas-ing the membrane area (Fig. 11). A reduction in theltration area is achieved by using smaller rotatingdisks. Since the radial position of the membrane tipis smaller, the centrifugal force is reduced (Eq. (4)).

Also the feed side pressure increases.Membrane permeability is found to have a large

effect on back pressure (Fig. 12); higher permeabil-ities generate a higher back pressure. As perme-ability increases, less pressure is required to ow thesame amount of uid through the membrane. Hence,the pressure on the permeate side may more easily

Fig. 11. Variation of the dimensionless cumulative ow rate along the membrane as a function of membrane area (: SMDF; - - - -: RMDF).

exceed the feed pressure. Filters with high permeabil-ity should therefore be designed to operate at either ahigher ow rate or a smaller membrane area.

3.4. Effect of uid viscosity and clearance betweendisks

During ltration, the uid viscosity within the ves-sel may increase as the concentration of retained par-ticles increases. While membrane performance (i.e.local and global transmembrane pressure) appears tobe relatively insensitive to uid viscosity, the shearstress on the membrane surface is greatly affected byviscosity. An increase in viscosity reduces shear stress.Therefore, to maintain a shear stress high enough toavoid particle deposition, it may be necessary toincrease the RPM during the ltration.

An important design parameter is the clearance be-tween the rotary and stationary disk since clearance

is related to the amount of membrane area per unitof vessel volume (packing density). For the small-est clearance studied (1.14 10 2 cm), no signicantchange in membrane performance was calculated tooccur. However, clearance affects the shear stress sig-nicantly. Reduction in clearance is predicted to resultin a decrease in the shear stress on the membrane sur-


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Q0 overall throughput ow rate (m 3 s 1)r radial position (m) R R2 value ()r 0 radial position of the edge of washer (RMDF) or

retaining seal tip (SMDF) (m)v velocity (m s 1) z axial position (m)

5.2. Greek symbols

azimuthal position (rad) dynamic uid viscosity (Pas) uid density (kg m 3) rotational speed (s 1) turbulent kinetic energy (m 2 s 2)

viscous dissipation rate of turbulent kineticenergy (m 2 s 3)

pG global transmembrane pressure (Pa) pL local transmembrane pressure (Pa)

5.3. Subscript

azimuthal componentr radial component z axial component

References

[1] A.S. Jnsson, Inuence of shear rate on the ux duringultraltration of colloidal substances, J. Membr. Sci. 79 (1993)9399.

[2] M.C. Aubert, M.P. Elluard, H. Barnier, Shear stress inducederosion of ltration cake studied by a at rotating disk method: Determination of the critical shear stress erosion, J.Membr. Sci. 84 (1993) 229240.

[3] N. Ohkuma, T. Shinoda, T. Aoi, Y. Okaniwa, Y. Magara,Performance of rotating disk modules in a collectedhuman excreta treatment plant, Wat. Sci. Tech. 30(4) (1994)141149.

[4] J.A. Engler, M.R. Wiesner, C. Anselme, Treatment of PACslurry using rotating disk membrane, In Proc. of 1995Membrane Technology Conference, Reno, NV, USA, vol. 1,1995, pp. 747758.

[5] S.S. Lee, A. Burt, G. Russotti, B. Buckland, Microltration of recombinant yeast cells using disk dynamic ltration system,Biotechnol. Bioeng. 48 (1995) 386400.

[6] U. Frenander, A.S. Jnsson, Cell harvesting by cross-owmicroltration using a shear-enhanced module, Biotechnol.Bioeng. 52 (1996) 397403.

[7] SpinTek introduces small centrifugal crossow ultraltrationsystem, Membrane and Separation Technology News 10 (12)(1992).

[8] B. Culkin, A. Plotkin, M. Monroe, Solve membrane foulingproblems with high-shear ltration, Chem. Eng. Prog., (1998)2933.

[9] Theory manual of FIDAP 7.0, Fluid Dynamics International,Evanston, IL, USA, pp. 2.312.39.

[10] J.W. Chew, Computation of Flow and Heat Transfer in

Rotating Disc System, Theoretical Science Group, RollsRoyce, Derby, UK, 1987.

[11] M. Williams, W.C. Chen, G. Bache, A. Eastland,Methodology of internal swirling ow systems with a rotatingwall, J. Turbomachinery 113 (1991) 8390.

[12] J.A. Engler, Investigation of membrane ltration in arotating disk geometry: use of computational uid dynamicsand laboratory evaluation, Doctoral thesis, Rice University,Houston, TX, USA, 1997.

[13] R.B. Bird, W.E. Stewart, E.N. Lightfoot, TransportPhenomena, Wiley, New York, 1980.

[14] J.W. Daily, R.E. Nece, Chamber dimension effects on inducedow and frictional resistance of enclosed rotating disks, Trans.ASME: J. Basic Eng., 1960 pp. 217232.

[15] L. Rudniak, S. Wronski, Laminar ow hydrodynamicsof rotating dynamics lters, Chem. Eng. J. 58 (1995) 145150.

[16] H. Schlichting, Boundary-layer Theory, McGraw-Hill, NewYork, 1968.

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