CFD modeling of hydrodynamic characteristics of slug bubble flow in a flat sheet membrane bioreactor

Journal of Membrane Science 445 (2013) 15–24

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CFD modeling of hydrodynamic characteristics of slug bubble flow in a flat sheet membrane bioreactor Peng Wei a, Kaisong Zhang a,n, Weimin Gao b, Lingxue Kong b, Robert Field c a

Institute of Urban Environment, Chinese Academy of Sciences, Xiamen 361021, China Institute for Frontier Materials, Deakin University, 75 Pigdons Road, Geelong, Victoria, 3217, Australia c Department of Engineering Science, University of Oxford, Oxford OX1 3PJ, UK b

art ic l e i nf o

a b s t r a c t

Article history: Received 6 February 2013 Received in revised form 17 May 2013 Accepted 19 May 2013 Available online 5 June 2013

It has previously been shown experimentally that the use of intermittent slug bubbling through the periodic introduction of large bubbles is an effective strategy to control fouling in MBRs. As the current set of experimental results is limited, a numerical study on the properties of a single bubble rising in an industrial flat sheet MBR was undertaken. A three-dimensional simulation with the volume of fluid (VOF) method was implemented. The predicted bubble is of a typical spherical cap shape which is consistent with experimental observation. The variation of the predicted shear stress on the membrane surface also shows good agreement with previous electrochemical results. Compared with the film region, the shear stresses in the wake region of the bubble were more intense and covered a much larger area. Additionally, the dominant component of shear stress is parallel with the bubble rising direction. For a fixed 100 mL bubble, the averaged shear stress attains a maximum value when the gap between the membranes is around 8 mm. With increasing activated sludge viscosity, the averaged shear stress increased only slightly. A brief review of CFD modeling and associated experimental work on two-phase flow in various membrane modules is included. & 2013 Elsevier B.V. All rights reserved.

Keywords: Flat sheet MBR Slug bubble Bubble size Effect of gap CFD

1. Introduction Gas sparging inducing two-phase flow has proven to be an effective and a reasonably economical strategy for oxygen transfer, mass transfer enhancement and fouling mitigation in submerged membrane bioreactor (MBR) systems [1]. It is well-known that air bubbling provides substantial flux enhancement in membrane processes, and a considerable amount of data have been provided to demonstrate its beneficial effects in a number of model systems with different kinds of membrane materials, as reviewed by Cui et al. [2]. Whilst other recent studies concerned with air sparging have confirmed the benefits on flux enhancement and/or selectivity for various different flat sheet membranes [3–8], there is increasing concern with regard to energy costs [9–11] and consequently increasing interests in anaerobic waste water treatment processes [12]. It is thus timely to consider ways of reducing aeration costs in aerobic MBRs, which are inherently more stable and smaller than anaerobic MBRs. In industrial applications of aerobic MBRs, aeration inducing two-phase flow in flat sheet MBR units is critical for fouling control and hence filtration performance

n

Corresponding author. Tel/fax: +86 592 6190782. E-mail address: [email protected] (K. Zhang).

0376-7388/$ - see front matter & 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.memsci.2013.05.036

especially as backwash is not an option due to the nature of the membranes. Previous electrochemical experimental results in a flat sheet membrane unit [13,14] indicated that periodic slug bubbling could simultaneously give a substantial reduction in air usage whilst achieving better hydrodynamic characteristics than free bubbling. In flat sheet MBRs it might provide an alternative method combining effective fouling control with economical energy consumption [15]. However due to the limitation of experimental conditions, the information on wall shear stress and relative mass transfer was limited to certain regions of the surface. Thus the detailed hydrodynamic characteristics on the whole membrane surface of flat sheet membrane, as induced by of slug bubbling, was still unclear. It is well-known that slug flow is of significance in two-phase flow regimes in terms of heat and mass transfer enhancement. In the last decade, there have been many reports on the hydrodynamic characteristics of slug bubbles in capillaries or tubes [16–21]. For computational fluid dynamics (CFD) modeling of twophase flow, different algorithms were implemented, including finite difference method [22], boundary integral method [23], and finite element method [24]. The volume of fluid method (VOF) has been found to be an effective tool for tracking the gas– liquid interface of slug flow [17–21,25]. These encouraging CFD modeling results have shed light on its application in membrane

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Table 1 Summary of CFD modeling and associated experimental work on two-phase flow in various membrane modules. Module type

Simulation model

Corresponding experiment

Highlight

CFD Modeling of slug flow ultrafiltration process to understand and quantify the details of flux enhancement resulting from gas sparging. Tubular Lab-scale, 200 kDa MWCO, tube horizontally Modeling gave a complete description of horizontal and mounted, bubble size and frequency controlled inclined flows. CFD results agreed well with published data. Experimental work to assess flux enhancement with defined bubbling in a horizontal tube. Tubular 2D, Eulerian two-fluid model, VOF and Model validation with previous experimental Examination of wall flux effect on flow field. Combined a combined model, uniform grid data on bubble shape and velocity. model gave the best results. Need for extremely fine computational meshes. Tubular 2D, axisymmetric, VOF, non-uniform Lab-scale, vertical tube, electrochemical shear Considered the effect of variable gas slug sizes, typical of grid probes for surface shear measurement commercial-scale tubular membranes. Experimental conditions significantly affected gas slug coalescence. Tubular 2D, VOF, non-uniform grid An universal dynamic spectrometer for sludge Characterized the hydrodynamics of sludge–gas flow in viscosity measurement contrast to water–gas flow and its influence on permeation. Hollow 3D, single fiber, single-phase flow, Lab-scale, single and dual-phase flow, Developed the electrochemical probe in submerged fiber uniform grid cylindrical baffle electrochemical shear probes single and multi-fiber systems. CFD analysis provided insight of single-phase flow field to illustrate shear force acting on a single-fiber surface. CFD model accounting for aeration, sludge rheology and 3D, full-scale plants, Eulerian two-phase Tracer studies were used to measure RTD of Hollow geometry was applied to each full-scale MBR, Results each full-scale MBR, The pilot-scale hollow fiber and model, coupled with sludge transport, were successfully validated against experimental data. fiber MBR operated for sludge rheology flat sheet no porous media for modules The effect of sludge settling and rheology had a minimal assessment. impact on the bulk mixing. Demonstrated an experimental approach to measure Hollow 3D, full-scale plant, Eulerian two-phase Lab-scale for inertial resistance calibration, fiber model, porous zone for modules resistance measured by separate directions in flow resistance of the fiber bundles. CFD model coupled with porous media obtained more accurate various flow conditions hydrodynamic descriptions of full-scale plant 3D, single-phase flow and VOF, X-ray computer tomography (CT) scans used A novel CFD approach based on CT scans and pressure Hollow unstructured quadrangular grid for geometry model development loss correlations were used to obtain patterns in fiber membrane units with irregular fiber arrangement. bundles Realistic information and an understanding of the global Hollow 3D, Eulerian multiphase model, porous Pilot-scale and large-scale, particle image flow dynamics in the MBR pilot and plant systems as velocimetry (PIV) technique, high-speed fiber medium model, unstructured well as plant geometry optimization. camera tetrahedral grid Flat sheet 2D, VOF, uniform grid, single Lab-scale, a video system for image recording Slug bubble motion and shape details determined by NF, momentum equation solved image analysis. 0.1 m2, Lab-scale, baffles inserted, different operating Various hydrodynamic factors considered, including Flat sheet 3D, Eulerian two-fluid model, nonparameters applied baffles. Identifying the most effective flow profiles for MF, uniform grid, mass and momentum fouling control. CFD results evaluated via corresponding 0.1 m2, equations for each phase shear stresses. Kubota Flat sheet 3D, Eulerian two-fluid model, uniform Lab-scale, two baffles enable an angle change Main resistance due to cake formation. CFD results MF, grid showed a high correlation with resistance data. Specific 0.11 m2, baffle angle had significant impact on shear stress Kubota Flat sheet 3D, VOF, non-uniform grid, mass and Different bubble sizes, good agreement with Successful simulation of slug bubble in flat sheet MBR MF momentum equations for each phase previous experiments channel. Shear stress in wake region was more intense. Optimal gap was obtained. Activated sludge viscosity effect found to be minor. Tubular

2D, VOF, axisymmetric, uniform quadrilateral grid, polarization and osmotic model 3D, VOF, laminar flow, slug in horizontal and inclined pipes

A good agreement between model for flux prediction and previous experiment.

process, especially in MBRs and so there has been an increasing number of reports on the hydrodynamic characteristics of slug bubbles in various membrane modules, both by CFD modeling, as well as associated experiments [6–8,26–37]. A summary is given in Table 1. This shows that compared with the comprehensive modeling results of tubular and hollow fiber membrane systems, there has been few corresponding fundamental studies for the flat sheet system. To our knowledge, the only one concerned with flat sheet systems [32] examined the mixing characteristics of fullscale systems which in not an issue that we have addressed. In this paper, the industrial application of flat sheet MBRs is addressed via 3D simulation and in particular the wall shear stress on the surface of flat sheet membrane was calculated. The previous experimental results obtained via electrochemistry [13] were used to validate the modeling results. The distributions of wall shear stress and the averaged/change of the wall shear stress were evaluated, particularly regarding the effects of bubble size and the gap between two flat sheets. Additionally the impact of

Refs.

[26]

[30]

[28]

[29]

[31]

[27]

[32]

[37]

[33]

[34,36]

[6]

[7,8]

[35]

This study

the viscosity of the activated sludge mixture with different mixed liquor suspended solids (MLSS) concentrations was also evaluated.

2. CFD model development As one of the main MBR modules, flat sheet membranes are different from tubular and hollow fiber membrane units with regard to CFD modeling. The tubular or capillary systems can be regarded as 2D, axisymmetric and use made of a moving coordinate, which simplifies the computation domain and saves computational time. However, as the aim was to obtain the hydrodynamic characteristics both inside the flat sheet module and on the whole flat sheet membrane surface, a 3D simulation was conducted and in particular the wall shear stresses on the membrane surface were calculated. The membrane size was the same as the one used in the experiments of Zhang et al. [13], which makes it comparable with an industrial unit. In order to

P. Wei et al. / Journal of Membrane Science 445 (2013) 15–24

investigate the hydrodynamic effect of different gaps, the gap width between two flat sheet membranes had one of four values: 20 mm, 10 mm, 8 mm, or 6 mm. 2.1. Governing equations The modeling was based on two-phase flow and the Volume of Fluid (VOF) method [38] was used for gas–liquid interface tracking. The simulation was implemented by solving hydrodynamic governing equations, including mass and momentum conservation equations, and additional equations for turbulence and interface tracking. Homogeneous flow was assumed for each phase, and the resulting velocity field was shared among both phases. Mixture properties of density ρ and dynamic viscosity μ depended on the volume fraction α of the qth phases, which were defined as ρ ¼ ∑αq ρq

ð1Þ

μ ¼ ∑αq μq

ð2Þ

17

The liquid volume fraction αL was calculated as αL þ αG ¼ 1

ð8Þ

Surface tension effects along the interface were considered and calculated via the continuum surface force (CSF) model [41]. In this model, surface tension acts as the source term in momentum equations, in terms of the pressure jump across the surface (Eq. 9). ! The surface tension F vol of two phases can be expressed as a

The mass and momentum conservation equations can be expressed as ∂ρ ! þ ∇ðρ u Þ ¼ 0 ∂t

ð3Þ

! ! ∂ðρ u Þ !! ! þ ∇ðρ u u Þ ¼ −∇p þ ρ g þ ρ F þ ∇! τ ∂t

ð4Þ

To consider the effect of turbulence induced by the rising bubble, the realizable k–ε model [39] were chosen for the bulk solution of each phase. In this model, k is the turbulence kinetic energy and ε is the turbulence dissipation rate, the realizable k–ε model equations are expressed as
 μef f ∂ðρkÞ ! þ ∇ρ u k ¼ ∇ ðμk þ Þ∇k þ μef f S2 −ρε ð5Þ ∂t sk
   μef f ∂ðρεÞ ρε2 ! pffiffiffiffiffi þ ∇ρ u ε ¼ ∇ μk þ ∇ε þ C 1 Sρε−C 2 ∂t sε k þ νε

Fig. 1. The structure and boundary conditions of the flat sheet model used in the simulations.

ð6Þ

where 2

k μef f ¼ C μ ρ ; qffiffiffiffiffiffiffiffiffiffiffiffiε S ¼ 2Sij Sij ;   1 ∂ui ∂uj Sij ¼ ; þ 2 ∂xj ∂xi
 η ; C 1 ¼ max 0:43; ηþ5 k η¼S ; ε C 2 ¼ 1:9; sk ¼ 1:0; sε ¼ 1:2 Cμ is not constant as it in the standard k–ε model [40], but is a function dependent on mean strain, rotation and turbulence fields. The standard wall functions are used to bridge the viscosityaffected region between the wall and the fully-turbulent region. The VOF method is suitable to model the motion of large bubbles in liquid. It tracks the interface between the two phases by the additional volume fraction equation [38]. Considering immiscible phases, the volume fraction αG can represent the volume fraction of gas phase in each cell. Additionally, no mass transfer between liquid and gas was considered. Thus its volume fraction equation can be established as ∂ ! ðαG ρG Þ þ ∇ðαG ρG u G Þ ¼ 0 ∂t

ð7Þ

Fig. 2. Mesh distribution. (a) Front view i.e. membrane surface view and (b) sideview note finer grid (on right side) close to membrane surface.

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volume force as follows pL −pG ¼ sκ ! 2ρκ∇αG F vol ¼ s ðρL þ ρG Þ

ð9Þ ð10Þ

where ρ is the volume-averaged density, which has been defined as Eq. (1), and κ is the surface curvature defined in terms of divergence of the unit normal, n^ κ ¼ ∇n^ n^ ¼

n ; n ¼ ∇αG jnj

ð11Þ ð12Þ

2.2. Discretization and numerical methods In order to capture the bubble motion through the rectangular cross-section, a 3D simulation was chosen. The first order implicit time-marching scheme was used for unsteady formulation solution. The modeling was carried out using CFD commercial software Fluent (Release ANSYS Fluent 13.0.0, 2010), which is based on the finite volume method. Water was the primary phase and air was the secondary phase, and they were assumed to be isothermal with constant properties. The piecewise linear interface calculation (PLIC) scheme [42] was chosen for interpolation treatment of the interface between gas and liquid phases. The following schemes were applied for governing equation discretizations to improve calculation accuracy and quality. A second order upwind scheme was chosen for momentum, k and ε equations discretization, and PRESTO! (pressure staggering option) scheme for pressure term discretization. The pressureimplicit with splitting of operators (PISO) scheme was used for pressure–velocity coupling, which is beneficial for calculations and convergence improvements of unsteady flows. 2.3. Model geometry and boundary conditions The domain design was consistent with an industrial flat sheet MBR module and a 3D coordinate system was built. Symmetric boundaries were used to reduce the computation size and to improve accuracy given a certain number of grids. The final

domain was determined to be a quarter of the original module with two symmetric planes, as shown in Fig. 1. The justification for the first line of symmetry shown in Fig. 1 is experimental; the intermittently injected slug bubbles were observed to rise along the center line [13]. The initial domain size was 150  600  10 mm (the third dimension was subsequently changed). Both the domain and grid cells were hexahedral. After grid independency tests, the grid distribution was selected as 100  120  14. Fig. 2 shows grid distribution of the refined regions. The region nearby the membrane surface was divided into five sub-layers to gain the properties of flow field and shear stress near the membrane (Fig. 2b). Half of the domain next to the left-right line of symmetry, which was the dominant region for bubbles rising, had increased grid density (Fig. 2a). To investigate the effects of slug flow on the shear stress at the membrane surface, simulations with various single large bubbles of different sizes rising in a stagnant liquid were carried out. The velocity of liquid at the inlet was set to zero and the outlet had an outflow condition. Two plates were set to provide symmetric conditions. The other boundaries were all stationary and there was a no fluid-slip condition at the membrane surface. The bubble shape was initialized as a cylinder perpendicular to the membrane surface with a height of 8 mm, so that different bubbles could be initialized by using different cylinder radii. An initial rise velocity of 0.2 m/s was set as an initial condition. The time step was of the order of 10−4 s, as the Courant number was controlled to be below 0.25. The total simulation time was around 1.0 s, by which time the bubble had reached its steady-state shape. 2.4. Data analysis and model verification The previous electrochemical results [13] were used to validate the results of CFD modeling. The hydrodynamic characteristics of slug bubble flow in a flat sheet module were measured by the limiting current method at various locations. The mass transfer coefficients could be related to the mean wall velocity gradient and diffusion coefficient [43] and hence the wall shear stresses at various positions were obtained. In order to compare with experimental results, two parameters were defined as in previous work [13]. Shear stress A represented the averaged shear stress enhancement and shear stress B was the maximum change of

Fig. 3. Comparison of the simulated bubble shape (with gas volume fraction over 90%) with an experimental bubble (The inlet bubble size is the same: 100 mL. The size of the experimental flat sheet unit is 300  1000  20 mm.).

P. Wei et al. / Journal of Membrane Science 445 (2013) 15–24

19

Fig. 4. Predicted wall shear stress parameters (Pa) on the membrane surface and the corresponding experimental results for A and B (μA) [13] for (a) at the central point and (b) at the same height.

3. Results and discussions

shear stress. These expressions are defined as follows A¼

1 n ∑ðτ −τ0 Þ n 1 i

B ¼ τmax −τ0

3.1. Model confirmation

ð14Þ

where τi is the shear stress at any point, τmax is the maximum shear stress and τ0 is the base shear stress without any bubbling.

As shown in Fig. 3, the shape of the simulated bubble is similar to that found previously in the corresponding flat sheet MBR unit. A large spherical cap was clearly formed, with several tiny bubbles following the main body. The simulation results of wall shear stress variation induced by different bubbles are shown in Fig. 4,

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Fig. 4. (continued)

which also gives a comparison with experimental data. The averaged wall shear stress of both central point and the whole surface increased with the bubble volume, which was similar to the experimental data [13]. It can be seen that the averaged shear stress (Wall shear stress A) was divided into two parts. It increased rapidly as bubble size increased from 5 to 60 mL, and then increased slowly as bubble volume was increased to 200 mL. This result demonstrated a critical bubble volume (around 60 mL) which was necessary for a good A value. The predicted variation of maximum shear stress (Wall shear stress B) was somewhat different from the experimental data because the max shear stress increment seemed to be linear as bubble size increased, while the experimental result still had two distinct regions. The shear stress variation at the same height shows a similar tendency (Fig. 4b). The main difference was the prediction of the variation maximum shear stress with bubble size, which represents the maximum mass transfer rate. However, considering that the experimental apparatus had some limitation, such as the system for returning the displaced water back to the unit (to ensure constant volume) which might affect the maximum shear stress, the overall results are considered satisfactory. The main limitation of the experimental apparatus was the tube radius of the recycle line which was not large enough to ensure rapid recycle when the bubble was large. This restriction might result in a weakening of the shear stress intensity in the experiments when bubbles beyond 100 mL were injected. Also in the simulation the velocity of liquid at the inlet was set to zero which differs from that in the experiments, and this might have led to an artificial intensification of the shear stresses (due to internal circulation) in the simulations. Overall a satisfactory verification was achieved particularly for bubbles up to 100 mL and therefore the model was used to give further insight into flux enhancement. 3.2. The effect of bubble size on wall shear stress 3.2.1. Wall shear stress on the whole membrane surface Fig. 5 shows the steady shear stress distribution on the whole membrane surface with respect to the indicated bubble location.

For a 25 mL bubble, the bubble only occupied one third of the membrane width, but the induced shear stress covered half of the width and was more intense in the wake region. For a bubble beyond 60 mL, the shear stress influence covered the whole space width. There were two shear stress peaks, one was located near the projection of bubble rim in the liquid film region, and the other was in wake region. The latter was much larger indicating a strongly dominant wake region. The area of shear stress effect induced by the wake region was much larger than that of the liquid film region, and it was more obvious as the bubble size increased. When bubble increased from 60 mL to 200 mL, the shear stress area affected by the wake region enlarged from 35% to around 65% of the whole domain. And the 200 mL bubble also induced more intense shear stress within its area. Moreover, the distribution of shear stress on membrane surface was more complex in the wake region. At any instance the shear stresses in the wake region included some regions with very low values which indicated the rapidly fluctuating nature of shear stresses in the wake. As noted by Cabassud et al. [44], mixing or turbulence near the membrane surface seems to control the flux enhancement and these are more intense with a 60 mL bubble than with a 25 mL one.

3.2.2. Wall shear stress at a specific position on the membrane surface Fig. 6 shows the change of wall shear stress on the central line as a single bubble passes through. It revealed that wall shear stress variation can be divided into two parts. The first part was related to the falling film and the wall shear stress increased linearly up to a local peak value located at the bubble tail. Next the wall shear stress decreased and then increased again to another higher peak before decreasing to zero. This second part is connected to the wake region and it covered a larger region. This tendency was quite similar to the current change induced by different bubbles rising at the same point according to the experimental results [13]. Both the CFD simulation and the electrochemical results indicate

P. Wei et al. / Journal of Membrane Science 445 (2013) 15–24

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Fig. 5. The calculated distribution of shear stress (Pa) on the whole membrane surface. (a) 25 mL, (b) 60 mL, (c) 200 mL. (Left: contour map of shear stress; right: the corresponding bubble shape and position).

the importance of the effect of the wake region behind the slug bubble. In the bubble region the mass transfer in the liquid film region is governed by laminar flow whilst there is turbulent flow elsewhere. The wake region creates more intense mass transfer enhancement than the region around the bubble itself and this is consistent with the electrochemical results. The shear stresses of X (horizontal) and Y components (vertical) at the central position were also calculated and are shown in Fig. 7a and b, respectively. It was found that both components had changes in direction. For the X component (Fig. 7a), the values varied in a disorderly manner, had absolute values smaller than 0.75 Pa and as such were almost insignificant compared with the Y component. Notable directional changes happened in the Y component when a bubble passed. In the liquid film region, the Y component of shear stress was opposite to the direction of the bubble rising. It increased nearly linearly from bubble nose to tail, but dropped sharply to zero. Then it started to increase in the opposite direction in the wake region up to another peak value before finally it dropped to nearly zero as the wake region faded. 3.3. The effect of gap between membranes on the wall shear stress Fig. 8 indicates the influence of gap width on the shear stress at the membrane surface. It was found that the averaged shear stress of 100 mL bubbles was larger than that of 60 mL bubbles for each gap size. When the gap was reduced from 20 mm to 8 mm, the averaged shear stress induced by 60 mL bubble increased, so did that of the 100 mL bubble. As the gap was further reduced to 6 mm, the average shear stress started to decrease. This implied

Fig. 6. The spatial variation of wall shear stress on the central line of the membrane surface for various bubble sizes.

there might be an optimal gap width around 8 mm to obtain a maximum shear stress effect. Thus it is interesting to note that others have found experimentally that as the gap was increased from 7 mm to 14 mm, the fouling became worse and the degree of fouling reduction by two-phase flow decreased by at least 40% [7]. For a 100 mL bubble, the results of 6, 8 and 10 mm gaps were different from the 20 mm ones, as the initial bubble tends to break up in the smaller gaps; this is a random process. Fig. 9 shows a typical image of bubble rising in the 6 mm gap with corresponding shear stress distribution on membrane surface. It was found that

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Fig. 9. The shear stress (Pa) distribution after the break-up of a bubble with an initial volume of 100 mL, (6 mm gap).

Table 2 Properties of three dominant phases on condition of 20 1C, water, activated sludge mixture 1 (ASM 1) and activated sludge mixture 2 (ASM 2). Dominant phase

MLSS (mg/L)

Density (kg/m3)

Viscosity (10−3 Pa s)

Surface tension coefficient （10−3 N/m）

Water ASM 1 ASM 2

0 2900 3700

998.2 994.7 997.2

1.003 1.050 1.110

72.75 70.60 70.04

Fig.7. Variation with position of the shear stresses at the central point of the flat sheet membrane surface for various bubble sizes. (a) X component, horizontal and (b) Y component, vertical.

Fig. 10. The averaged shear stresses in water and activated sludge mixtures.

3.4. Effect of viscosity on shear stress in MBR system

Fig. 8. The effect of gap on the wall shear stress for two different bubble sizes, 60 mL and 100 mL. (100 mL bubble in 10 mm gap).

when two bubbles rise up in parallel, the high values of shear stress were not only in the central region between the bubbles but also close to the boundaries as shown in Fig. 9. Given this pattern, it is clear that having a gap width that gives some break-up of large bubbles is desirable.

In order to simulate the shear stress induced by a slug bubble in an actual MBR system, the effect of viscosity, as well as surface tension, on wall shear stress was evaluated for different activated sludge mixtures. MBR mixtures with different MLSS concentrations were adopted as a substitute for water. Their properties are shown in Table 2, in conjunction with those for pure water. Fig. 10 shows the averaged shear stress values of 100 mL bubble in water and activated sludge mixtures for a 10 mm gap. It was found that the averaged shear stress value in ASM systems was slightly larger as its viscosity was larger. However, the wall shear stress increase was slight (2.9%), compared with the increase in viscosity (10.7%) which reflects the turbulent nature of the flow. Fig. 11 confirms this finding for three different bubble sizes. Thus the modeling of the shear stress distribution in

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23

Nomenclature C2 ! F ! F vol g k n^ p S, Sij t ! u,u x y

Fig. 11. Shear stress parameter A for water and activated sludge mixture 1 (ASM 1) for three different bubble sizes (10 mm gap).

air-water systems is valid as a model for actual activated sludge systems. 4. Conclusions This paper presented the results from a numerical study of single slug bubble rising in a flat sheet module. 3D CFD simulations of a single slug bubble rising in flat sheet module were evaluated and compared with the previous electrochemical experimental data for intermittent slug bubbling. The main findings were: 1. The modeled steady bubble was found to have a spherical cap shape, with small bubbles dragged away from the rim, which was in agreement with observation. For gap of 10 mm or less there was a tendency for large bubbles of 100 mL to break into two which created three regions of high shear. 2. Up to a certain bubble size the predicted average shear stress increased rapidly at first and then more slowly. The evaluated A parameter was in agreement with experimental findings. 3. The wake region provided the main region of high shear stress and for bubbles of 60 mL and above there was excellent spanwise production of shear stresses above 1.0 Pa. The areas of higher shear stress were larger and more intense in the wake region than in the film region. This explains the experimental observation of a continuous enhancement effect resulting from the passage of an intermittent bubble. 4. The gap size was found to affect the wall shear stresses significantly. There may be an optimal gap width, around 8 mm, for an industrial flat sheet MBR unit, to obtain a maximum shear stress effect, in agreement with previous experimental observations. 5. The averaged shear stress increased slightly with increasing liquid viscosity but the effect was minor and therefore water can usefully be used as the model for the dominant phase.

Acknowledgments The authors gratefully acknowledge the financial support by the Knowledge Innovation Project of Chinese Academy of Science (Project no. KZCX2-YW-452) and the National Nature Science Foundation of China (Grant no. 50708090). RWF thanks the Chinese Academy of Sciences for the Distinguished Visiting Professor Fellowship. The authors are also grateful to the reviewers and the editor for their helpful comments.

turbulence model constant default, 1.9 external body force, N volume force in CSF model, N acceleration due to gravity, m/s2 turbulence kinetic energy, m2/s2 unit normal vector to the surface pressure, Pa strain rate, strain rate tensor component, 1/s time, s vector velocity, velocity, m/s horizontal coordinate, m vertical coordinate, m

Greek symbols α μk μeff ν ρ s sk sε κ ε ! τ,τ

volume fraction dynamic viscosity, Pa s turbulent viscosity, Pa s kinematic viscosity, m2/s density, kg/m3 surface tension, N/m Prandtl number for turbulent kinetic energy, 1.0 Prandtl number for turbulent dissipation rate, 1.2 surface curvature turbulence dissipation rate, m2/s3 shear stress, Pa

Subscripts G i, j L q

gas phase different coordinates liquid phase qth fluid phase

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