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Improved Mass Transfer Performance of Membrane units in a Toroidal Helical Pipe—reduction of concentration polarization by secondary flows
Abstract
We evaluate a Toroidal Helical Pipe (THP) for the extent of process intensification that it can offer over an equivalent length of straight pipe by providing continuous curvature changes resulting in complex secondary flows in a compact space. The present study is a radical departure from traditional curved and helical tubes with constant curvatures as they often lead to a fully-developed state. The THP results in a continuously varying curvature. Here we examine the application of THP for membrane transport, where reducing the concentration polarization is a challenge. We build the geometry from a 3d space curve represented by C(t;R,r,n)=[(R+r·cosnt)·cost,(R+r·cosnt)·sint,r·sinnt], where R is the radius of the torus, r is the radius of the pipe, and n is the number of turns of the helical pipe around the torus. Although this enables a design optimization study over the geometric parameter space (R,r,n), we restrict our study to the following values C(t;5,1.2,7).The computational model is used to study solutions for a Reynolds number of up to Re=100 and a Peclet number of Pe=6×104. We demonstrate a significant reduction in the concentration polarization aided by the secondary flows with increasing Re. The permeate flow increased by 33% at Re=100.
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Membrane distillation (MD) is a promising technology to treat mine water. This work aims to investigate the change in mass and heat transfer in reverse osmosis mine water treatment by vacuum membrane distillation (VMD). A 3D computational fluid dynamics (CFD) model was carried out using COMSOL Multiphysics and verified by the experimental results. Then, response Surface Methodology (RSM) was used to explore the effects of various parameters on the permeate flux and heat transfer efficiency. In terms of the influence degree on the permeation flux, the vacuum pressure > feed temperature > membrane length > feed temperature membrane length, and the membrane length has a negative correlation with the membrane flux. Increasing the feed temperature can also increase the convective heat transfer at the feed side, which will affect the heat transfer efficiency. Furthermore, the feed temperature also has a critical effect on the temperature polarization phenomenon. The temperature polarization becomes more notable at high temperatures.
Simulation via Computational Fluid Dynamics (CFD) offers a convenient way for visualising hydrodynamics and mass transport in spacer-filled membrane channels, facilitating further developments in spiral wound membrane (SWM) modules for desalination processes. This paper provides a review on the use of CFD modelling for the development of novel spacers used in the SWM modules for three types of osmotic membrane processes: reverse osmosis (RO), forward osmosis (FO) and pressure retarded osmosis (PRO). Currently, the modelling of mass transfer and fouling for complex spacer geometries is still limited. Compared with RO, CFD modelling for PRO is very rare owing to the relative infancy of this osmotically driven membrane process. Despite the rising popularity of multi-scale modelling of osmotic membrane processes, CFD can only be used for predicting process performance in the absence of fouling. This paper also reviews the most common metrics used for evaluating membrane module performance at the small and large scales.
In the face of water shortages, the world seeks to explore all available options in reducing the over exploitation of limited freshwater resources. One of the surest available water resources is wastewater. As the population grows, industrial, agricultural, and domestic activities increase accordingly in order to cater for the voluminous needs of man. These activities produce large volumes of wastewater from which water can be reclaimed to serve many purposes. Over the years, conventional wastewater treatment processes have succeeded to some extent in treating effluents for discharge purposes. However, improvements in wastewater treatment processes are necessary in order to make treated wastewater re-usable for industrial, agricultural, and domestic purposes. Membrane technology has emerged as a favorite choice for reclaiming water from different wastewater streams for re-use. This review looks at the trending membrane technologies in wastewater treatment, their advantages and disadvantages. It also discusses membrane fouling, membrane cleaning, and membrane modules. Finally, recommendations for future research pertaining to the application of membrane technology in wastewater treatment are made.
In this work, we study the implementation of electrically-driven flow (EDF) models in the finite-volume framework of $\text{OpenFOAM}^\circledR$. The Poisson-Nernst-Planck model is used for the transport of charged species and it is coupled to the Navier-Stokes equations, governing the fluid flow. In addition, the Poisson-Boltzmann and Debye-H\"uckel models are also implemented. The discretization method and the boundary conditions are carefully handled in order to ensure conservativeness of ionic species in generic meshes and second-order accuracy in space and time. The applicability of the developed solver is illustrated in two relevant EDFs: induced-charge electroosmosis around a conducting cylinder and charge transport across an ion-selective membrane. The solver developed in the present work, freely available as open-source, can be a valuable and versatile tool in the investigation of generic electrically-driven flows.
The efficiency of conventional heat exchangers is restricted by many factors, such as effectiveness of convective heat transfer and cost of operation. The current research deals with these issues by developing a novel method for building a lower-cost yet more efficient heat sink. This method involves using a specially designed curved microchannel to utilise the enhanced fluid mixing characteristics of Dean vortices, and thus transferring heat efficiently. Numerical models have been employed to investigate the heat transfer enhancement of curved channels over straight equivalents, with the aim of optimising the heat exchanger design based on the parameters of maximising heat transfer whilst minimising pressure drop and unit cost. A range of cross-sectional geometries for the curved channels were compared, showing significantly higher Nusselt Numbers than equivalent straight channels throughout, and finding superior performance factors for square, circular and symmetrical trapezoidal profiles. Due to the difficulty and expense in manufacturing circular microchannels, the relatively simple to fabricate square and symmetrical trapezoidal channels are put forward as the most advantageous designs. The variation of Nusselt Number over the length of the channel for a range of different curvatures (and hence Dean numbers) is also examined, showing significantly higher heat transfer occurring in areas where the generated Dean vortices are strongest. The variation in Nusselt Number was found to form the shape of an 'arc'. In this way, a relationship between the Dean Number and the Nusselt Number is characterised and discussed, leading to suggestions regarding optimal microfluidic heat transfer design.
The analysis of flow fields and heat or mass transfer phenomena is of great importance in the optimum design of spacer-filled channel geometries for a variety of membrane-based processes. In the present work, models of spacer-filled channels often adopted in Membrane Distillation are simultaneously investigated by experiments and Computational Fluid Dynamics (CFD). Experiments rely on a non-intrusive technique, based on the use of Thermochromic Liquid Crystals (TLC) and digital image processing, and provide the local distribution of the convective heat transfer coefficient on a thermally active wall. CFD relies on steady-state (laminar flow) simulations in the lower end of the Reynolds number range investigated and on direct numerical simulations in the upper end of this range. This latter is a region of great practical interest for real applications, in which the flow is chaotic but not fully turbulent, and neither steady-state simulations nor the use of turbulence models would provide satisfactory predictions. Results are reported and discussed for a specific spacer geometry (overlapped orthogonal cylindrical filaments) and different spacer orientations with respect to the main flow. To the authors' knowledge, this is the first study in which an experimental validation of computational results concerning local heat or mass transfer is performed for spacer-filled channels.
Two-fluid Dean vortex flow in a coiled pipe with vanishing torsion, and its effect on the mass transfer through the liquid-liquid interface of two immiscible fluids are studied numerically. The liquids are stratified by gravity, with the denser one occupying the lower part of the pipe. The Navier-Stokes equations in both fluid layers are solved numerically by the finite volume method. The results reveal a detailed structure of the transverse flow (the Dean vortices) in coiled pipes with the dimensionless curvature 0.1. Both cocurrent and countercurrent axial flows in the fluid layers are considered. Using the flow fields predicted, the mass transfer equation is solved. It is shown that the mass transfer of a passive scalar (say, a protein with the Schmidt number of the order of 103) through the interface can be significantly enhanced by the Dean vortices, so that the mass transfer rate can be increased by three to four times. This makes the Dean vortex flow an effective tool for mass transfer enhancement at the liquid-liquid interface. It is shown that the Dean flow provides a stronger mixing than the Taylor-Couette flow. It is also shown that there exists an optimal axial flow rate in terms of this enhancement. The optimal flow corresponds to the value of the Dean number of about 180. In the countercurrent flow case the Dean vortices can split, which has a negative effect on the mass transfer enhancement. Both the cocurrent and countercurrent axial flows yield a similar enhancement effect on the interfacial mass transfer rate. The problem is related to the search for novel bioseparator devices.
The iodide–iodate chemical probe method is modified by a novel adaptive procedure to investigate the mixing abilities of two compact curved-duct reactors. Both reactors have a rectangular cross section; the first has smooth curvature (called the wavy duct) and the second has sharper bends (zigzag duct). In the conventional procedure, this method is used to characterize local micro-mixing, and for all experiments (for different Reynolds numbers and injection points) the reagent initial concentrations are kept at the same values. Even with wall injection, the selectivity of the chemical system is generally improved by increasing the flow Reynolds number. Nevertheless, two limitations encountered in using chemical probes (with the conventional protocol) to characterize the mixing abilities of the present reactors that prevent the conventional protocol of the chemical probe from discriminating between the mixing abilities of the two mockups. First, the duct walls are corrugated, so that the wall injection used to measure local micro-mixing is affected by the wall roughness, independently of the Reynolds number. Second, the flow Reynolds numbers are relatively low due to the small size of the duct sides, so that the measurements are inevitably hindered by meso-mixing effects. The challenge is thus to adapt the chemical method for characterizing the global mixing, by enlarging the measurement volume so as to capture and take into account all mixing scales. In the new adaptive procedure, the kinetics of the second reaction are adjusted in such a way as to impose the same reactive volume for different Reynolds numbers, leading to more relevant results for the segregation index XS. Experimental results reveal that the mixing performance of the zigzag channel as assessed by this method is slightly above that of the wavy one. Finally, the segregation index in both reactors is related to the mixing time tm by using a physical model in the literature.
The present work examines chaotic mixing as a means of enhancing the in-tube convection heat transfer in helical coils. It is shown that simple modifications of coil geometry can be made to take advantage of this phenomenon. The study focuses on a geometry with the axis of the coil being turned through 90-degrees in a periodic manner, and comparisons are made with a coil without this change in axis. Particle paths are calculated using the classical perturbation solution of Dean for the secondary flow. Chaotic mixing is confirmed by a positive Lyapunov exponent. The temperature field is calculated numerically showing that chaotic mixing is responsible for considerable flattening of the temperature profile and an increase in convective heat transfer. Experiments are conducted with water on two coiled tube geometries over a Reynolds number range of 3000-10000. The coils are identical in every respect except that one is conventional with constant axis, while the other is with alternating axis. The latter shows a 6-8% higher in-tube heat transfer coefficient due to chaotic mixing, with a corresponding pressure drop increase of 1.5-2.5%.
The potential industrial applications of curved tubes for single- and two-phase flow are reviewed within the context of physics of flow, trends in the development of technology, and its laboratory to industrial-scale commercialization. Comparison of the performance of curved tube configurations demonstrates its edge over the conventional motionless mixers, heat exchangers, and reactors. Alongside, their respective advantages and limitations are also highlighted. Further, a compendium of the available correlations for single- and two-phase friction factor and heat- and mass-transfer coefficient in curved tubes has also been presented. Key issues regarding the design parameters governing the performance of the curved tubes for mixing and heat- and mass-transfer that impact the research, development, and scale-up or scale-down of such devices are also analyzed. Emerging trends for the development of a new class of curved tubes, namely, inverters and serpentine and chaotic devices are also presented.
We examine the effectiveness of the forced convective heat transfer in a toroidal helical pipe (THP), as a compact process intensification device for use in heat exchangers. Earlier, we showed that mixing was enhanced significantly in such devices due to continuously changing curvature along the length of the pipe while retaining its compactness. In this work, we examine six Reynolds numbers ranging from 1 to 200, two Prandtl numbers (1 and 7), and two thermal boundary conditions (fixed-temperature and fixed-flux). The heat transfer efficiency in THP is quantified mainly by the Nusselt number as a function of the downstream distance, and it is compared with that in straight pipes of identical setup. Thus, the enhancement by the geometric factor alone is extracted. We found in THP the Nusselt number is not monotonic but varies periodically around mean values that can be more than four times higher than straight pipes. The unique coupled-Dean vortex flow pattern, due to the varying curvature of the THP axis, significantly enhances the in-plane mixing and causes the higher and oscillatory Nusselt numbers.
The accuracy and stability of implicit CFD codes are frequently impaired by the decoupling between variables, which can ultimately lead to numerical divergence. Coupled solvers, which solve all the governing equations simultaneously, have the potential to fix this problem. In this work, we report the implementation of coupled solvers for transient and steady-state electrically-driven flow simulations in the finite-volumes framework. The numerical method, developed in OpenFOAM®, is generic for Newtonian and viscoelastic fluids and is formulated for the Poisson–Nernst–Planck and Poisson–Boltzmann models. The resulting coupled systems of equations are solved efficiently with PETSc library. The performance of the coupled solvers is assessed in two test cases: induced-charge electroosmosis of a Newtonian fluid around a cylinder; electroosmotic flow of a PTT viscoelastic fluid in a contraction/expansion microchannel. The coupled solvers are more accurate in transient simulations and allow the use of larger time-steps without numerical divergence. For steady-state simulations, the coupled solvers converge in fewer iterations than segregated solvers. Although coupled solvers are much slower in a per time-step basis, the overall speedup factor obtained in this study reached a maximum value of ∼100, where the highest factors have been obtained with semi-coupled solvers, which drop some coupling terms between equations. While further research is needed to improve the efficiency of the matrix solving stage, coupled solvers are already superior to segregated solvers in a number of cases.
In this paper we present the design of a novel, passive mixer, to enhance mixing and residence time distribution for promoting transport and reaction mechanisms in such devices. The goal is to understand and optimize the flow patterns for enhancing mixing in laminar flows through toroidal helical pipes, inspired by the coiled flow inverter (CFI) (Saxena and Nigam, 1984). A toroidal helix is a smooth analytical curve winding around a torus. It is characterized by three parameters: the radius of the torus’ centerline, the radius of the torus’ cross-section, and the number of turns it winds around the torus. Unlike the torus or the straight helix which have constant curvatures, the toroidal helix has a spatially oscillating curvature. We found that this causes the otherwise separated pair of Dean vortices to couple together, periodically re-orient, shrink and grow within each turn of the pipe. The resultant complex streamlines span the entire cross-section and enhances mixing via advective means. By constraining the total pipe length, a meaningful comparison of mixing efficiency within a given volume of pipe can be assessed as the torus's cross-section radius and the number of helix turns are systematically varied. Reynolds number of up to 400 is explored with the number of turns of 3, 5, 7 and 8. The optimization study shows that the best mixing performance is achieved using a moderate number of turns. Apart from flow pattern and mixing efficiency, we also studied the pressure drop to monitor increased energy consumption and residence time distribution of the flow to monitor degree of mixing.
Computational fluid dynamics simulation was carried out for three-dimensional desalination modules containing triangular and square ribs attached to the membrane surface. The solution-diffusion membrane transport model was applied along the surface of the corrugated membrane. The membrane flux model which couples the water permeation rate with local salt concentration impose a selective removal of components in the feed channel. The local water flux, salt concentration, wall shear stress, and Sherwood number were monitored over the surface of membranes to determine effects of eddy promoter corrugations on mitigation of concentration polarization and the total water flux. Simulations are conducted using a laminar model for Reynolds number of 100 and k-ω SST turbulence model for Reynolds number of 400 and 1000. Mathematical model and numerical methods employed are validated by comparing predictions against measurements reported earlier. Predicted results agree quantitatively and qualitatively with previous experimental results for membranes with semi-circular cross-sectioned ribs. The results show that corrugated membranes especially triangular chevrons enhance membrane performance profoundly at all flow rates. Water permeation rate is increased, concentration polarization is alleviated, and the potential fouling in the module is reduced by introducing corrugated membranes.
Hydrodynamics and mass transfer characteristics in an industrial spiral wound reverse osmosis (RO) feed channel under typical plant operating conditions are investigated using fully-coupled three-dimensional computational fluid dynamic (CFD) simulations with a detailed spacer geometry. The pressure drop vs average longitudinal velocity can be approximated by ΔPc∝ū1.67 and the trend matches an empirical correlation previously derived from plant data. Substantial wall-parallel velocity near the membrane surface is observed, which suppresses boundary layer development. Rolling cells are formed in the center of the feed channel, which promote transverse mixing. Different from concentration polarization phenomenon in unobstructed flat channels, concentrated islands are isolated in regions near spacer filaments where flow is relatively stagnant. The local mass transfer coefficient km oscillates longitudinally but the cell-average k¯m appears fairly constant in cells adjacent to each other. It is shown that k¯m∝ū0.40 under typical plant operating conditions. A one-dimensional system-level model incorporating the CFD results is developed and validated by plant trial data under various operating conditions, yielding a slight improvement in accuracy as compared to the author's previously published empirical model.
A computational study has been conducted to examine three-dimensional steady multicomponent fluid flows in the reverse osmosis membrane module. The module contains a net of spacers. The SST k-ω turbulence model is employed to simulate flow and concentration fields at Re = 400 and 800, while the laminar model is employed to characterize flow and concentration fields at Re = 100. Spacer grids with 30°, 45° and 60° are considered as three different geometries. The membrane is treated as a functional surface where water flux, concentration and local pressure are coupled. The nature of concentration polarization in each membrane module is determined. Characteristics of potential fouling buildup are determined from the wall shear stress distribution. Correlations between potential fouling regions and the concentration distribution are presented. The coefficient of performance for each membrane module is determined at all flow rates considered. It has been illustrated that all membrane modules perform better at higher flow rates. The membrane module containing the net of spacers in the 30° arrangement is shown to be the most efficient membrane module. This study proves that the configuration of spacers is an important optimization parameter for the design of reverse osmosis membrane modules.
The present study offer a novel coiled flow inverter (CFI) membrane module for higher permeate flux without consuming extra material or energy, compared to helical coiled membrane module. The proposed CFI membrane module is fabricated by bending of helical coil at 90° with equal arm length before and after the bend. The mass transfer and shear stress in CFI membrane module are also compared with straight tube module in addition to the helical coiled membrane module, for two different gas liquid contact systems viz oxygenation and carbonation. The Sherwood number increases by 10 – 20% for oxygenation and up to 26% for carbonation process in CFI membrane module as compared to helical coiled membrane module, under identical process conditions. The mass transfer in CFI membrane module augments because of the reduced radial gradient caused by intensified radial flow due to the complete flow inversion. The CFI membrane module offer 3.5 – 5.5 fold enhancement in Sherwood number. The number of merits of CFI module has been observed up to 2.5 for oxygenation and 2.7 for carbonation process, as compared to the straight tube module. The literature data on different helical coil membrane modules have been revisited over wide range of design parameters and an empirical correlation is proposed for Sherwood number.
Spacer-filled channels are employed in membrane modules in many industrial applications where feed-flow spacers (employed to separate membrane sheets and create flow channels) tend to enhance mass transport characteristics (and possibly) mitigate fouling and concentration polarization phenomena. In this work direct numerical simulation was performed for the flow in spacer-filled channels to obtain a better understanding of fluid flow phenomena in these assemblies. Reynolds numbers of 300, 500 and 800 were considered. The effect of spacer location was also studied for three different configurations: spacer at the centre of the channel, off-centre, and attached to the wall. Instantaneous velocity fields and flow structures, such as boundary layer separation on the walls and on the cylinder, eddies on the walls, recirculation regions and vortex shedding were investigated. A Fourier analysis was carried out on the time series velocity data. Using this analysis the Strouhal number was calculated and the development of the flow towards a broader turbulent state at higher Reynolds number was captured. Other statistical characteristics such as time-averaged velocities and wall shear rates are obtained and discussed. The average pressure loss was calculated for the channels and found to be highest for spacer at the centre of the channel and lowest for spacer attached to the wall.
The state of the art in modelling flow in curved tubes and pipes is assessed, with attention given to developing and fully developed flows, both steady and unsteady. Consideration is given to flows in infinitely coiled pipes, in finite bends, to multiphase flows, the flow of non-Newtonian fluids, the effect of flexible walls, and to thermal effects. The discussion centers on laminar incompressible flows and pipes and tubes with circular cross-sections. The fluid is considered viscousand asociated with a secondary flow resulting from centrifugal pressure gradient in the main flow influencing the stagnant fluid in the wall boundary layer. The significance of the Dean number is explored, together with the effects of different geometries, wall charcteristics, and fluid properties.
Features (micromixers) that promote chaotic mixing were fabricated on reverse-osmosis membrane surfaces and evaluated using computational models and laboratory experiments to determine their effectiveness in reducing biofouling. Computational fluid dynamics models of membrane feed channels were developed using different patterns of micromixers on the membrane surface. The shear-stress distribution along the membrane surface was simulated for steady flows along the different micromixer configurations. In addition, the hypothetical mass transfer of a tracer from the membrane surface was used as a metric to compare the amount of scouring and mixing in configurations with and without micromixers. Epoxy micromixers were printed directly onto membrane surfaces, and different patterns were evaluated experimentally. Fluorescence hyperspectral imaging results showed that regions of simulated high shear stress on the membrane corresponded to regions of lower bacterial growth in the experiments, while regions of simulated low shear stress corresponded to regions of higher bacterial growth. In addition, the presence of the micromixers appeared to reduce the overall biofouling concentration in one series of experiments, but the results were inconclusive in another series of experiments. These results indicate that while the enhancement of mixing and shear stress via micromixers may delay or mitigate the onset of localized membrane fouling from biofilms or other contaminants, the impact of micromixers on the overall performance of reverse-osmosis membranes needs further investigation. © 2008 American Institute of Chemical Engineers Environ Prog, 2008
Flatter velocity profiles and more uniform thermal environents are extremely desirous factors for improved performance in flow reactors and heat exchangers. One means of achieving this in laminar flow systems is to use mixers and flow inverters. These improve performance but at higher initial and operating costs. This paper introduces a new and more effective device for flow inversion which is achieved by changing the direction of centrifugal force in helically-coiled tubes. Transient response experiments carried out under the conditions of both negligible and significant molecular diffusion reveal drastic narrowing of the residence time distribution (RTD). The effectiveness of the present device can be assessed by the fact that even at a Dean number of 3 the value of dispersion number as low as 0.0013 is obtained under the condition of significant diffusion, and in the case of negligible diffusion the value of dimensionless time at which the first element of tracer appears at the outlet is as high as 0.85.
Coiled flow inverter is an innovative device, which works on the principle of complete flow inversion and centrifugal force. It was fabricated by introducing 90° bends in helical coils. It has two-fold advantage of intensifying the convective transfer processes (i.e. increase heat and mass transfer coefficients) and also provide increased transfer area per unit volume of space. It is very compact in size as compared to straight tubes and straight helix. Hence, it is a step towards process intensification. An experimental study was conducted for estimating the gas void fraction and flow patterns for gas–liquid two-phase flowing through this device. The coils were prepared using transparent PVC tubing of 0.005–0.015 m internal diameter with coil diameter varying from 0.08 to 0.2 m. A wide range of gas and liquid flow rates, 8.33 × 10−5 to 0.001 and 3.33 × 10−6 to 0.001 m3/s respectively were investigated. Sixteen coiled flow inverters of different geometric configurations were tested. Various flow patterns observed were stratified, slug, plug, wavy and churn flow. An empirical correlation for void fraction for laminar, transition and turbulent regimes were developed. Data from 7582 gas–liquid flow experiments in coiled flow inverter have been processed for power law and composite power law friction factor correlations to flow regime determination. Separate power law correlations for laminar and turbulent flows were obtained for all flow regimes in the database and also for different flow patterns. The results were compared with Lockhart–Martinelli correlation and Hughmark's correlation.
Simulation of Reverse Osmosis and Osmotically Driven Membrane Processes
- P Xie
Numerical Simulation of Concentration Polarization to Estimate Gypsum and Calcium Carbonate Scaling on Membrane Surfaces
- A Santafé-Moros
- J M Gozálvez-Zafrilla