Chemical Product and Process Modeling Volume 4, Issue 4 2009 Article 5 CHEMPOR 2008 Determination of the Wall Shear Stress by Numerical Simulation: Membrane Process Applications Fanny Springer Rémy Ghidossi Emilie Carretier Damien Veyret Didier Dhaler Philippe Moulin Université Paul Cézanne Aix Marseille, fanny.springer@etu.univ-cezanne.fr Polytech Marseille, Technopôle de Château-Gombert, remy.ghidossi@oenologie.ubordeaux2.fr Université Paul Cézanne Aix Marseille, Europôle de l Arbois, emilie.carretier@univcezanne.fr Polytech Marseille, Technopôle de Château-Gombert, damien.veyret@polytech.univ-mrs.fr NOVASEP APPLEXION SAS Site, didier.dhaler@novasep.com Université Paul Cézanne Aix Marseille, Europôle de l Arbois, philippe.moulin@univcezanne.fr Copyright c 2009 The Berkeley Electronic Press. All rights reserved.
Determination of the Wall Shear Stress by Numerical Simulation: Membrane Process Applications Fanny Springer, Rémy Ghidossi, Emilie Carretier, Damien Veyret, Didier Dhaler, and Philippe Moulin Abstract Membrane processes have been intensely developing during the last decades, and mainly in dairy industry. Considering the feed effluent complexity, concentration polarization phenomenon and fouling are accentuated limitations for the development of membrane dairy filtration processes. Knowledge of the wall shear stress developed at the membrane surface is fundamental to reduce those phenomena. In this work, the variation of the wall shear stress on cylindrical, square, triangular and hybrid channels by numerical simulation for various operating parameters was studied. Predictions were established for different commercial ceramic membranes and predict the geometry that tends to better mass transport efficiency by enhancing hydrodynamics conditions. Numerical simulations are performed over a typical range of Reynolds numbers inside different channel geometries under laminar and turbulent conditions. Consequently, this paper intended to enhance the performances of these processes by maximizing the average wall shear stress on the membrane surface by numerical simulation. A comparison with experimental results was realized and a good agreement was obtained. Given those conclusions, a new membrane according to the whole CFD results consistent with experimental results was designed. KEYWORDS: computational fluids dynamics, wall shear stress, channel geometry, ceramic membrane, fouling Please send correspondence to P. Moulin, tel (+ 33) 4 42 90 85 01; e-mail: philippe.moulin@univcezanne.fr.
Springer et al.: Wall Shear Stress Determination by Numerical Simulation 1. Introduction In dairy industry, microfiltration is more and more used for milk sterilization and casein separation. Ultrafiltration is currently the most widely spread process for applications as protein separation or milk composition standardization. Considering the feed effluent complexity, concentration polarization phenomenon and fouling are accentuated limitations for the development of membrane dairy filtration processes. The accumulation of materials near the membrane, with the deposition of colloids and suspended solids triggers the reduction of their performances. Fouling strongly depends on the wall shear stress that occurs from radial velocity gradient during the filtration step. So, better knowing the wall shear stress is fundamental to reduce the fouling phenomena. Enhancing turbulence at the membrane surface: Dean vortices [Moulin et al 1999], dynamic filtration [Koutsou et al 2004] and unsteady flows [Krstic et al 2002] enables indeed to increase the mass transfer coefficient and sweep the deposition at the surface [Noriatsu and Yamamoto 2001]. It was shown in previous works on the filtration of various effluents, that the limiting permeate flux was linked to the wall shear stress by a phenomenological relation J lim = Aτ n with J lim the limit permeate flux (m.s -1 ), and τ the wall shear stress (Pa) [Manno et al 1998; Moll et al 2007]. The simplified approach considered for this work was the higher the shear stress the higher the permeate flux. No mass transfer model was used. Thus, the objective was to find the channel geometry showing the optimal wall shear stress to reduce uttermost the fouling. The influence of the channel section was also determined and the membrane process parameters (transmembrane pressure (TMP), flow rate ) on the wall shear stress characterized. Given these results, the final purpose was to design the most appropriate membrane for the intended application. Appropriate is heard in the sense of a satisfactory production which implies optimal wall shear stress values among the studied commercial geometries. 2. Materials and Methods A large range of MF and UF cases was studied in this work for a more accurate prediction of the wall shear stress. For this aim, the numerical modelling tool appeared as the most appropriate one [Ghidossi et al 2006]. It permits to better apprehend complex mechanics and to reduce experiment number. Computational Fluid Dynamics (CFD) has become an effective tool to attain these objectives more quickly and cost effectively by solving the basic governing equations for fluid flow: - the continuity equation: Published by The Berkeley Electronic Press, 2009 1
Chemical Product and Process Modeling, Vol. 4 [2009], Iss. 4, Art. 5 ρ + ρu = 0 t (1) - the momentum transport equation: ( ρu ) + U ( ρu ) = P + μ( t 2 U ) (2) A three-dimensional coordinate system was used. Numerical simulations were made for high Reynolds numbers in complex geometries. RNG k-ε model was used for it appears in literature as preferentially used in turbulent flow. A segregated solver was used to deal with the previous equations (see Fluent for further details). A structured non-uniform grid was used to discretize the computational domain of the channels. On Figure 1 is shown an example of graded mesh. On average, 200,000 volume cells were included in each grid, which was refined near the wall with the intention of resolving the laminar sublayer. Comparison of the velocity at the center of the pipe and the location of the maximum velocity were studied for 4 different meshes in both non-uniform and uniform distribution. Depending on the grid refinement and type, the difference ranges within 0.1 to 3.0%. The graded mesh gave more accurate results than the uniform. Figure 1: Exemple of the graded mesh used for the square channel The wall was considered as impermeable. This assumption can be validated: (i) in ceramic membrane, the permeate flow is often lower than 2% of the circulating flow; (ii) it was shown that the wall shear stress can be calculated in permeable tube with the value obtained in no permeable tube and the value of permeate flow [Moll et al 2007]. A parabolic profile of the flow is assumed at the tube entrance. The flow shape is considered as developed at the outlet of the tube. Then, modelling results were confirmed by milk ultrafiltration experiments performed with multichannel ceramic membranes (length = 1.178 m). This http://www.bepress.com/cppm/vol4/iss4/5 DOI: 10.2202/1934-2659.1328 2
Springer et al.: Wall Shear Stress Determination by Numerical Simulation experimental campaign was also lead to better understand the effects of reversible and irreversible fouling as a function of membrane geometry. The exploitation of those results required to choose and take into account one parameter that best illustrated the membrane performances linked to the wall shear stress. The various resistances to mass transfer were calculated on the basis of the model of resistances in series. This resistance is the sum of three resistances to mass transfer: R = R + R + R t m i r (3) where R t represents the total resistance to transfer, R m the hydraulic resistance, R r the reversible resistance and R i the irreversible resistance. The reversible resistance is the resistance which is removed after simply rinsing the membrane and the filtration unit with water under controlled conditions. It was calculated at constant velocity and constant TMP with the formula: R t = TMP μ J P (4) This reversible resistance is linked to polarisation concentration phenomemon and is the most appropriate to illustrate the shear stress efficiency. 3. Results and discussion 3.1 Influence of the membrane channel geometry The raw simulation results enable to obtain the variation of the wall shear stress according to the section of the channel for different flow velocities. On Figure 2 are represented the characteristics of the wall shear stress for the different geometries studied, plotted versus the location in the channel along the dimensionless perimeter. A logical and periodic variation of wall shear stresses according to the perimeter is obtained for all inlet velocities and simulated geometries. As expected, the cylindrical geometry develops a constant wall shear stress. For geometries made of corners (triangle, square), the results obtained by numerical simulation prove that the distribution of wall shear stress presents a maximum which is located in the middle of the side and a minimal value at the angle for any rate of flow turbulent flow. Furthermore, Figure 2 shows that the variation of the wall shear stress on the triangular geometry has many analogies with those observed on the square Published by The Berkeley Electronic Press, 2009 3
Chemical Product and Process Modeling, Vol. 4 [2009], Iss. 4, Art. 5 geometry. Indeed, a maximum of wall shear stress is observed in the middle of each edge and decreases progressively until reaching a minimal value on the corner for a constant channel section. Considering only the maximal values of the wall shear stress, the optimal configuration is the triangular one and secondly the square and cylinder geometries. 300 250 triangle square cylinder Wall shear stress (Pa) 200 150 100 50 0 0 0,25 0,5 0,75 1 0.25 0.50 0.75 1 P/P 0 P/P 0 Figure 2: Variation of the wall shear stress along the dimensionless channel perimeter for the different geometries considered [v = 6 m.s -1, channel section 16 mm²] The simulations showed that there is no influence of the velocity on the ratio τ local /τ max. Only the geometry has an influence on this ratio and the importance of the dead zones created. Simulated results are synthesized on Figure 3 where the variation of the average wall shear stresses for different geometries is represented. It appears that the wall shear stress is reduced with increasing channel sections. The cylindrical geometry offers the highest values in term of wall shear stress for the smallest channel section (4.0 mm²). For larger channel sections, the triangular geometry is more advantageous. The square geometry shows weaker performances. It is possible to obtain the local values of the wall shear stress by numerical simulations and to calculate an average value on the perimeter. Given those studies, the most appropriate membrane prototype for the complex filtration process when it comes to dairy effluents can be designed: the Evolution prototype has a hybrid form channel. Considering the effluent of milk, which is strongly fouling and pressure losses triggering, large channel sections, i.e channel cross- http://www.bepress.com/cppm/vol4/iss4/5 DOI: 10.2202/1934-2659.1328 4
Springer et al.: Wall Shear Stress Determination by Numerical Simulation sectional areas, were chosen for industrial productivity reasons. The choice of the channel shape is justified by the efficiency of the triangular geometry for high values of channel sections. Nevertheless, the angles are subjected to a rapid fouling, which affects the process performances during the filtration step and the regeneration step. Consequently, the corners were rounded so as to obtain a heartlike channel shape, as shown on Figure 4, more likely to achieve industrial objectives. The advantage of our simplified approach is the global view of the system. Disadvantage is that predicting permeate flux is impossible and only comparisons can be carried out. An experimental campaign was used to validate this approach. 200 180 Cylindrical channel Square channel Triangular channel 160 Wall shear stress (Pa) 140 120 100 80 60 2 m/s 4m/s 2 6 m/s 40 20 0 1 2 3 4 5 6 7 8 9 4,01 12,6 28,3 4,01 12,6 28,3 4,01 12,6 28,3 Section Surface (mm 2 ) Figure 3: Variation of average wall shear stresses vs. channel sections for different geometries and different velocities Figure 4: Hybrid shape of the Evolution membrane Published by The Berkeley Electronic Press, 2009 5
Chemical Product and Process Modeling, Vol. 4 [2009], Iss. 4, Art. 5 3.2 Validation of the modeling results and comparison of commercial membrane performances The results of milk ultrafiltration campaigns are presented on Figure 5 for different commercial ceramic membranes (15 KDa) with various geometries and channel sections. The milk characteristics are given in Table 1. After the filtration step, the reversible resistance was experimentally measured after rinsing the membrane with soft conditions of pressure and velocity. This characteristic shows how the wall shear stress influences the reversible resistance whatever the membrane geometry or channel section considered. 90 Reversible resistance (x10-12 m -1 ) 80 70 60 50 40 30 20 10 27 channels (triangular) 52 channels (square) 19 channels (cylindrical) 7 channels (cylindrical) Evolution (hybrid) 0 0 20 40 60 80 100 120 140 160 Wall shear stress (Pa) Figure 5: Variation of the reversible resistance vs. wall shear stress for different membranes For all geometries, irreversible fouling also decreases with an increasing wall shear stress, so our simplified approach is validated. http://www.bepress.com/cppm/vol4/iss4/5 DOI: 10.2202/1934-2659.1328 6
Springer et al.: Wall Shear Stress Determination by Numerical Simulation Table 1. UHT milk composition Compounds Concentration (g.l -1 ) Glucids 49 Grease matter 39 Casein 25,6 Lactose 46 Calcium 1,2 Salt 9 Water 900 Density 1030 Moreover Figure 5 shows an identical behaviour of the reversible resistance according to the wall shear stress values given by simulation, whatever the membrane considered: this validates our simulation results. Furthermore, beyond a value of 70 Pa for the wall shear stress, the reversible resistance remains very low, so it is of high interest to privilege geometries that enable to reach such an average value of wall shear stress. The ultrafiltration experimental campaign makes it possible to compare the commercial membrane performances. The observations confirm that results can be determined by numerical simulation in order to compare the performances of the membranes. In order to take into account the specific surface area of each membrane, the flows produced by a module equipped with the membranes studied (99 membrane capacity) were calculated during the milk filtration. Figure 6 presents the results obtained for a TMP equal to 2 bars. The 52 channel membrane (0.5 m²) allows a greater production than the other membranes, because of the greater exchange area provided by this geometry. The choice of this geometry is coherent to achieve optimization, but it is confronted to the technological limits highlighted in our work: very small values of shear stress in the corner. With very close channel section values, and relatively to the same channel area, the comparison between the cylindrical (19 channels: 0.25 m², 7 channels: 0.16 m²) and hybrid geometries shows that the performances of the Evolution membrane are better (0.20 m²). Moreover, production improvement is due to a greater membrane surface area, which the Evolution membrane geometry provides. Triangular channels show interesting performances, partly explained by a higher membrane area (0.35 m²). Nevertheless, since corners trigger rapid fouling, cleanliness considerations must be made. As a consequence, better performances can be concluded from this new design methodology applied to the Evolution membrane. It was seen experimentally that production enhancement is more satisfactory with low tangential velocities, and these tangential velocities are usually used for the specific process of milk filtration. The other advantage of the Evolution Published by The Berkeley Electronic Press, 2009 7
Chemical Product and Process Modeling, Vol. 4 [2009], Iss. 4, Art. 5 membrane is the gradual variation of its wall shear stress, which never takes a null value. Indeed, the non homogeneous distribution of the wall shear stress is a serious handicap for membrane regeneration. Permeate flow (m 3.h -1 ) 3,5 3 2,5 2 1,5 1 52 channels (square) 27 channels (triangular) 19 channels (cylindrical) 7 channels (cylindrical) Evolution (hybrid) 0,5 0 0 1 2 3 4 5 6 7 Velocity (m.s -1 ) Figure 6: Variation of the permeate flow vs. tangential velocities for different membranes (TMP 2 bars) 4. Conclusion This modeling work relies on the simplified approach: the higher the shear stress is, the more satisfactory the permeate flux is. The variation of the wall shear stress according to the section of the channel was obtained from simulation results for different flow velocities under turbulent conditions. We compared the influence of different parameters such as the channel geometry, the channel section and the operating parameters on the process performances. The channel geometry was then optimized by maximizing the average wall shear stress on the membrane surface. In this study, the dairy feed effluent was chosen for its complexity: it triggers concentration polarization phenomenon and fouling which are accentuated limitations for the development of membrane filtration processes. A comparison with experimental results during milk ultrafiltration campaigns has been realised and a good agreement is obtained. Moreover an identical behaviour of the reversible resistance according to the wall shear stress values given by simulations, whatever the membrane considered, is showed. This validates our simulation results and modelling approach. So, this methodology is relevant to design new membrane geometries intended to specialized applications. Finally, a compromise between membrane area, channel geometry and energy consumption must be taken into account to optimize those processes. http://www.bepress.com/cppm/vol4/iss4/5 DOI: 10.2202/1934-2659.1328 8
Springer et al.: Wall Shear Stress Determination by Numerical Simulation Nomenclature J lim : limit permeate flux (m.s -1 ) J p : permeate flow of distilled water (m.s -1 ) P: location of a considered point on the channel perimeter (m) P 0 : channel perimeter (m) P/P 0 : dimensionless channel perimeter (-) R t : total resistance to the transfer (m -1 ) R m : hydraulic resistance (m -1 ) R r : reversible resistance (m -1 ) R i : irreversible resistance (m -1 ) TMP: transmembrane Pressure (bar) U: axial velocity (m.s -1 ) μ: dynamic viscosity (Pa.s) ρ: density (kg.m -3 ) τ: wall shear stress (Pa) References Ghidossi R., Veyret D., Moulin P. Computational fluid dynamics applied to membranes: State of the art and opportunities, Chemical Engineering and Processing (2006), Vol 45, 437-454. Koutsou C.P., Yiantsios S.G., Karabelas A.J. Numerical simulation of the flow in a plane-channel containing a periodic array of cylindrical turbulence promoters, Journal of Membrane Science (2004) Vol 231, 81-90. Krstic D.M., Tekic M.N., Caric M.D., Milanovic S.D. The effect of turbulence promoter on cross-flow microfiltration of skim milk, Journal of Membrane Science (2002) Vol 208, 303-314. Manno P., Moulin P., Rouch J.C., Clifton M., Aptel P. Mass transfer improvement in helically wound hollow fiber ultrafiltration modules: Yeast suspensions, Separation and Purification Technology (1998) Vol 14, 175-182. Moll R., Veyret D., Charbit F., Moulin P. Dean vortices applied to membrane process. Part II. Numerical approach, Journal of Membrane Science (2007), Vol 288, 321-335. Moulin P., Manno P., Rouch J.C., Serra C., Clifton M.J., Aptel P. Flux improvement by Dean vortices: ultrafiltration of colloidal suspensions and macromolecular solutions, Journal of Membrane Science (1999) Vol 156, 109-130. Noriatsu O., Yamamoto K. Hydraulic effects on sludge accumulation on membrane surface in crossflow filtration, Water Research (2001) Vol 35, 3137-3146. Published by The Berkeley Electronic Press, 2009 9