Direct numerical simulation of flow in spacer-filled channels: Effect of spacer geometrical characteristics

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Abstract

A numerical and experimental study is presented, aimed at obtaining a better understanding of transport phenomena in spirally wound membrane elements, where feed flow spacers are used to enhance mass transport characteristics and mitigate fouling and concentration polarization phenomena. Direct numerical simulations of the Navier-Stokes equations are performed in three-dimensional geometries which closely represent real spacer-filled membrane channels. A range of Reynolds numbers characteristic of such membrane modules is covered. The results obtained clearly suggest that a transition to unsteady flow occurs at relatively low Reynolds numbers. Qualitative flow features such as the development and separation of boundary layers, vortex formation, the presence of high shear regions and recirculation zones, and the underlying mechanisms are examined. In addition, quantitative statistical characteristics are obtained and compared for a range of spacer geometrical characteristics, including frequency spectra of flow fluctuations, as well as wall shear stresses and pressure drop. The latter are directly related to mass transport enhancement and can provide input to quantitative criteria for the optimization of spacer geometrical characteristics. Finally, pressure drop measurements are performed in a specially fabricated spacer-filled channel and the results show good agreement with the numerical predictions.

Introduction

Membrane processes are among the most advanced methods in water treatment and desalination. Spirally wound membrane modules are predominantly employed in reverse osmosis and nanofiltration, and they also find use in ultrafiltration and microfiltration. A characteristic of this type of modules is the presence of spacers in the feed flow and permeate channels. These feed flow spacers, which usually have the form of non-woven crossed cylinders, serve to separate adjacent membrane leaves and create flow passages, but also to promote flow unsteadiness and enhance mass transport. In this way, the undesirable fouling and concentration polarization phenomena are mitigated. In recent years the important role of membrane spacers has been recognized, and several experimental and theoretical studies have appeared aiming at understanding the underlying phenomena and optimizing spacer configuration. Today, with the development of powerful computational tools and high accuracy numerical methods, direct numerical simulation of turbulent flows in complex geometries is feasible for Reynolds numbers on the order of a few thousand. Thus, CFD is becoming a useful tool in studies aimed at optimizing spacer configurations.

Clearly, an improvement in spacer configuration must be judged on the basis of three aspects. The first is the enhancement of mass transport characteristics, which reduce concentration polarization and osmotic pressure at the membrane surface, as well as the potential for scaling. The second is the enhancement of shear stresses at the membrane surface in order to minimize the tendency of fouling species to deposit and reduce membrane flux and rejection or modify the feed channel hydrodynamics. The third aspect is the pressure drop which is associated with the energy expended for pumping and is contributing to the decreasing membrane productivity along an array of elements. This issue is more prominent in low pressure membrane applications (i.e. nanofiltration, UF). Probably a unique answer to such conflicting requirements does not exist, and tailor-made spacers need to be employed for different types of membranes or applications and feeds. For example, for low salinity, low pressure applications the role of osmotic pressure may not be predominant, but pressure drop and fouling or scaling may be. Finally, it must be stressed that the issues of mass transfer coefficients and shear stress fields on the membranes must be considered not only in an average sense, but also in terms of their spatial variation. It is well known in this respect that the pattern of fouling deposits is uneven and closely follows the geometric pattern of spacers.

Several well known early experimental works in spacer-filled channels exist, with or without membranes, which deal with flow hydrodynamics, pressure drop and mass transport [1], [2], [3], [4], [5], [6], [7]. Schock and Miquel [1] studied various commercial spacers and developed dimensionless correlations for pressure drop and mass transfer coefficients. The latter were obtained by employing a concentration polarization model. Permeate channel spacers were also an important aspect of their study. Correlations of the usual formf=a1RebandSh=a2RecScd,were obtained for the friction factor and Sherwood number. As expected, spacer-filled channels exhibited significantly higher mass transfer rates compared to empty channels over the same range of Reynolds numbers, albeit at increased pressure drop. However, significant differences could not be discerned between the various spacers used in their tests. Kuroda et al. [2] measured pressure drop and also employed an electrochemical technique to obtain mass transfer coefficients in channels with non-permeable walls; correlations were obtained of the form indicated above. Furthermore, they attempted to correlate the coefficients a1 and a2, in terms of the spacer geometrical characteristics. However, their results appear to neglect the effect of spacer orientation with respect to the mean flow, which is important, as evidenced by many experimental and theoretical studies in the literature that are discussed below. The latter suggest that if spacer filaments are roughly aligned with the mean flow, lower pressure drop and mass transfer coefficients are obtained. This is born out in the experiments of Winograd et al. [3], performed in an electrochemical cell, in the experimental results of pressure drop measurements in spacer-filled channels of Farkova [4], as well as those of Zimmerer and Kottke [5], who employed gas flow and a technique of ammonia adsorption and reaction on wet filter paper to measure mass transfer coefficients. Furthermore, it was shown in the latter paper that the overall flow pattern changes with orientation of the filaments between the extremes of a zig-zag (or corkscrew) and a channeling pattern, where flow is reflected on the channel side walls. Similar behavior is born out in the experiments of Feron and Solt [6], who studied flow features and stability for various idealized and realistic geometries of inserts. Belfort and Guter [7] tested various commercial spacers for electrodialysis use. They evaluated spacers in terms of porosity, dead flow area capability, stack resistance and pressure drop and they proposed some optimal spacer configurations. Moreover, flow visualization experiments revealed flow features generated by various spacer designs and the existence of a vortex screw-like motion which diminishes the thickness of the mass transfer boundary layer.

Significant work has been carried out in the last decade by Fane, Wiley and coworkers [8], [9], [10], [11], [12], [13], [14], [15], [16], [17], [18], [19]. This work includes experiments with commercial and laboratory-made spacers to obtain pressure drop and flux [8], [9], [10] as well as mass transfer coefficients of UF membranes [8], [9]. In addition, they performed studies of solute rejection and coupling between concentrate and permeate channels that also take into account variable fluid properties due to concentration polarization [11], [12], fouling observations with microparticles in spacer-filled channels [13], as well as economic evaluation of various spacer configurations [8], [9], [10], [14]. A novel spacer design with improved characteristics was also proposed [14]. Working with idealized geometries comprised of a set of parallel filaments, as well as with a variety of commercial spacers, Da Costa and Fane [10] showed that filaments attached to the membrane and transverse to the mean flow (the ladder-type spacer) are more effective in reducing concentration polarization and more economically attractive than filaments aligned with the flow. They also suggested that an optimum mesh length exists [10]. In a recent study of membrane fouling with microparticles Neal et al. [13] observed that fouling was more pronounced when the filaments were oriented transversely to the mean flow. This suggests that different fouling species, i.e. scaling salts, organics, colloids or aggregates and microparticles may behave differently and a universal optimal spacer for all types may not exist. Several numerical studies of flow and mass transport in various idealized geometries have been also performed [15], [16], [17], [18], [19]. Various arrangements of a limited number of filaments (up to five) have been studied by employing turbulence models [15] or DNS techniques [11], [12], [16], [17], [18], [19]. Flow separation and unsteadiness, as well as vortex shedding have been simulated and analyzed. The results of the numerical simulations agree qualitatively with the main findings of experimental studies outlined above, namely that optimum values exist for mesh size and filament orientation. However, all the above computational work is limited to 2-D geometries and flows.

Two-dimensional simulations of rather more fundamental character in channels containing “eddy promoters” were also performed by other researchers. Karniadakis et al. [20] in a theoretical study of eddy promoters for heat transfer enhancement studied the flow in a plane-channel, where a periodic array of small-diameter cylinders is placed. They report that the presence of the small cylinders leads to the destabilization of the flow by essentially the same mechanisms as in a plane-channel but at greatly reduced Reynolds numbers. These are close to 150, as compared to approx. 5800 for a plane-channel. Relevant to turbulence promotion are also the studies of Chen et al. [21] and Zovatto and Pedrizzetti [22], who treat various geometric configurations of a single cylinder located in a plane-channel and analyze flow features and stability. Kang and Chang [23], performed numerical simulations of the mass transfer of a two-dimensional flow in channel containing two types of spacers (zig-zag and cavity). Their model was steady state and apart from making a description of the flow features generated by both types of spacers, they calculated local Sherwood numbers at the channels walls. They also performed flow visualization experiments in order to test the validity of the numerical results and concluded that there is a good agreement for low Reynolds numbers. Koutsou et al. [24] studied the 2-D flow in a channel containing a periodic array of symmetrically placed cylinders and analyzed the flow topology, flow transition to periodic and chaotic states, as well as quantitative characteristics such as wall shear stress and pressure drop and Reynolds stress distribution.

Significant contributions in understanding transport phenomena in nanofiltration have been also made by de Pinho and coworkers [25], [26], [27], [28], [29]. Thus, simulations successfully describing experimental observations of fluid flow, concentration polarization and solute rejection of nanofiltration membranes have been presented. The studies relevant to spacers are limited to a 2-D ladder type configuration [28], [29]. It is interesting that these studies take permeation through the membrane into account, and thus they are rather unique in this respect. In agreement with previous studies, it is predicted that overall mass transport enhancement and concentration polarization reduction is better if the filaments of the ladder type spacer are attached on the membranes rather than on the opposite side of the channel, as well as compared to an empty channel.

Several theoretical studies have focused closer to the membrane spacer configurations by performing three-dimensional simulations of realistic spacer geometries. Karode and Kumar [30] were the first that described the 3-D structure of several commercial spacers and the flow domain in a realistic manner. They simulated flow in a spacer-filled channel similar to the one used by Da Costa et al. [9] in their experiments. The channeling flow pattern observed before [5], [6], [7] could be reproduced by the simulations. The spacers were evaluated in terms of pressure drop and shear stress on the membrane surfaces. However, this work was limited to steady state simulations without indication of the range of Reynolds numbers where a steady state exists. It is noted that the simulation of such an extended flow field inevitably results in a limited spatial resolution. More recently, modified spacer designs were numerically tested in terms of low pressure drop and high strain rates and some of the new designs appear to be promising [31], [32], [33].

Li et al. [34], [35] presented studies of flow and mass transfer by performing three-dimensional direct numerical simulations in a geometry closely representing membrane spacers. Periodic boundary conditions were employed, thus enabling them to simulate just one cell of the pattern formed by the spacer. The effect of spacer geometrical characteristics was studied and optimal parameters were proposed. Although no information about the spatial and temporal resolution of these results was provided, experimental data of averaged mass transfer coefficients appeared to support their simulations [35], [36]. They also tested new spacer designs for mass transfer enhancement compared to the performance of a spacer which was concluded to be optimal in a previous work [35]. The developed spacer designs should ensure the co-existence of longitudinal and transverse vortices (which result in higher mass transfer coefficients) and minimal cross flow power consumption. The approach was mainly experimental and one of the new designs was found to be promising [37].

The aim of the present paper is to make a contribution towards improving the understanding of hydrodynamic and mass transport phenomena in spacer-filled membrane channels and the optimization of spacer characteristics. A range of spacers with systematically varied geometrical characteristics is covered both numerically and experimentally, in order to assess their merits and drawbacks as regards mass transfer enhancement and reduction of energy consumption. In Section 2 the geometrical and physical parameter space is defined and details on the computational aspects of the study are presented. In addition, the experimental set-up to obtain pressure drop measurements is described. Direct numerical simulations of the transient Navier-Stokes equations are performed, and the results are carefully validated in terms of grid independence and analyzed. In Section 3, the qualitative flow features are identified and discussed, and the quantitative characteristics, such as pressure drop and wall shear stress, are obtained and compared. Emphasis is also placed on the spatial distribution of the time-averaged quantities and their fluctuations in order to identify localized regions of inferior membrane performance in terms of concentration polarization.

Section snippets

Parameters of the study

Typical membrane spacers are considered to be composed of two sets of straight non-woven parallel cylindrical filaments, as shown in Fig. 1. The geometrical characteristics are the ratio of the distance between parallel filaments to the filament diameter (L/D), the angle between the crossing filaments β, and the flow attack angle α.

Usually the ratio L/D varies between 7 and 9 [1], [5], whereas the angles α and β are in the range of 0° to 90° and 60° to 120°, respectively [30], [31], [32], [33],

Qualitative flow features

For all the geometries considered the numerical simulations revealed some generic qualitative flow features or a flow topology which is discussed below. In Fig. 8 fluid particle path lines are shown, obtained from a simulation at a low Reynolds number where steady state conditions prevail. Fluid streams enter the unit cell through the constrictions below cylinder 1 and above cylinder 2. In a similar fashion, fluid exits through the constrictions below cylinder 3 and above cylinder 4. These

Conclusions

Direct numerical simulations of the flow in spacer-filled channels have been carried out over a range of Reynolds numbers characteristic of the operation of actual membrane elements. These simulations do not repeat the results of previous theoretical studies but significantly extend them covering an unexplored part of the dimensionless parameter range of geometrical spacer characteristics. The results obtained suggest that a transition to unsteady flow occurs at relatively low Reynolds numbers;

Acknowledgement

This work is supported by the Middle East Desalination Research Center, under contract no 04-AS-002.

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