Computational fluid dynamics modelling of sewage sludge mixing in an anaerobic digester

Advances in Engineering Software 44 (2012) 54–62

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Computational fluid dynamics modelling of sewage sludge mixing in an anaerobic digester J. Bridgeman ⇑ School of Civil Engineering, University of Birmingham, Edgbaston, Birmingham B15 2TT, UK

a r t i c l e

i n f o

Article history: Available online 24 June 2011 Keywords: Sewage sludge Digestion Biogas CFD Non-Newtonian fluid Turbulence Energy

a b s t r a c t In this paper, the development of a computational fluid dynamics (CFD) model to simulate the mechanical mixing of sewage sludge at laboratory scale is reported. The paper recommends a strategy for modelling mechanically mixed sewage sludge at laboratory scale. Generated flow patterns are analysed and conclusions drawn as to the effectiveness of mixing in the laboratory scale digester. Data relating biogas yield to different mixing regimes are reported and combined with CFD model results. From this, novel conclusions regarding velocity gradients and biogas yield are drawn. Ó 2011 Civil-Comp Ltd and Elsevier Ltd. All rights reserved.

1. Introduction Renewable energy resources produce very little carbon or other greenhouse gases and consequently their development is an integral part of the UK Government’s strategy for reducing carbon emissions. Currently, the UK water industry generates 493 GW h of renewable energy each year, equating to 14% of the total energy used to treat water and municipal sewage in 2006. Anaerobic digestion is the most widespread technology for the treatment of sewage sludge, the by-product of sewage treatment. This natural process uses bacteria to break down biodegradable material and produces a biogas rich in methane. The current drive to maximise energy recovery means that the biogas from anaerobic digestion is increasingly harnessed by means of combined heat and power technology. There exists, therefore, the need to optimise the performance of anaerobic digestion vessels in order to maximise energy recovery. Sewage sludge digesters and, indeed, other organic waste digesters, are tanks with minimal internal fittings, in which feedstock (e.g. sewage sludge, agricultural slurry, food waste) is maintained at constant temperature, mixed with anaerobic bacteria and reduced to a methane-rich biogas. Mixing energy is thought to account for approximately 20% of the total energy input of digesters in temperate climates; the remainder being used for sludge heating where required. The primary aim of mixing is to ensure phys-

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ical, chemical and biological uniformity in a digester and to minimise grit deposition. Although a well-designed sludge digester has in the past been synonymous with a well-mixed digester, the associated energy and resource costs are significant. Plant designers and operators now seek the minimum degree of mixing to minimise cost and environmental impact without compromising biogas output. Some sewage sludge digesters are mixed for just 5 min in an hour without any apparent detriment to biogas yield, whereas others are continually mixed to achieve similar biogas yields. A small base of research suggests that anaerobic bacteria could even work more effectively in stratified (unmixed or partially mixed) digesters where they form close associations that enable rapid and efficient processing of waste to biogas; even producing more biogas than their continually-mixed counterparts, while having a considerably reduced energy input. The limited evidence base suggests that continual mixing might not be necessary (and might even be detrimental) for maximising sludge conversion to biogas. It also suggests that not all parts of a digester need to be mixed equally, with unmixed strata at the base of the digester demonstrating methane producing activity 1.5 times of that in mixed zones. In order to predict confidently the optimum mixing regime for a particular sludge digester, it is necessary to determine to what extent biogas output depends on, and can be influenced by, flow patterns in a digester; flow patterns which are in turn determined by physical parameters of the digestion vessels, inflow mode, mixing systems and sludge rheology. Thus, mixing regimes for sludge digesters could be tailored to encourage flow patterns that would potentially increase biogas production and/or reduce mixing

0965-9978/$ - see front matter Ó 2011 Civil-Comp Ltd and Elsevier Ltd. All rights reserved. doi:10.1016/j.advengsoft.2011.05.037

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J. Bridgeman / Advances in Engineering Software 44 (2012) 54–62

energy input; in both cases improving the overall energy yield from that digester and reducing its environmental impact. The work reported in this paper is an integral, first stage of a longer term project to assess digester mixing efficiency and design, and its link with biogas yield. In view of the complexity and size of full-scale anaerobic digestion plants, analysis of process performance and optimisation is often conducted at laboratory scale. In this study, digestion was undertaken in a 6 l cylindrical vessel which was continuously stirred by two, six-blade paddles, which were positioned towards the bottom and top of the tank (Fig. 1). Details of vessel and impeller geometry are provided in Table 1. The stirrer speed was controlled, and set to various mixing speeds in the range 20–200 rpm. The overall aim of the work reported in this paper was to assess the hydraulic performance of the lab scale digester under different sludge loading criteria and different mixing speeds. This paper is an updated and revised version of the conference paper [1]. The paper has been strengthened via inclusion of additional mesh geometry details, amendments to the model validation description (including the addition of computational effort), and an improved assessment of the relationship between sludge solids content and vessel dead volume. 2. CFD modelling of sewage sludge 2.1. Model development 2.1.1. Computing facility and models Computational fluid dynamics (CFD) is an accepted and wellused means of assessing and optimising process designs without necessarily incurring the expense of prototype development. Recent years have seen an increase in the application of CFD to water

Table 1 Vessel and impeller geometry.

Diameter (mm) Height (mm) Thickness (mm) Offset (from base to impeller centreline) (mm)

Vessel

Impeller 1

Impeller 2

160 305 – –

70 55 3 197.5

70 55 3 47.5

industry issues. However, the use of CFD to model the flow and mixing of organic wastes (such as manure) and sewage sludge has been rather more limited [2–7]. The analyses reported here were undertaken using the commercially-available codes, Gambit 2.2.30 for mesh construction, and Fluent v6.3.26 (Ansys, Sheffield, UK). All simulations were undertaken using the high performance computing facility at the University of Birmingham, UK. This HPC, known as BlueBEAR is a compute cluster consisting of 256 nodes, each of which is an IBM x3455, and each one containing two 64 bit AMD opteron duel core processors; i.e. 1024 cores, with a filestore of 70 Tera Bytes. Steady state flow fields were developed for the laboratory digester mixing either water or one of five different total dissolved solids (TDS) contents sludges (2.5%, 5.4%, 7.5%, 9.1% and 12.1% TDS) at 100 rpm. In addition, models were developed to mimic the flow fields generated in the vessel when filled with 5.4% TDS sludge and mixed at 30, 50, 100 and 200 rpm (5.4% being selected as it is indicative of thickened municipal sewage sludge fed to anaerobic digesters). 2.1.2. Turbulence model selection Modelling of turbulent flow fields in a constrained vessel with rotating elements is a challenging process. For this work, the performance of five turbulence models (Standard k–e (Sk–e), Realizable k–e (Rk–e), Renormalised Group k–e (RNG k–e), Standard k– x (Sk-x), and Reynolds Stress Model (RSM)) were assessed. Two treatments of the rotating mesh (sliding mesh, SM, and multiple reference frames, MRF) were assessed using the Rk–e model; however, it quickly became apparent that the computational expense of using the sliding mesh treatment was too great in this instance. Further details of the turbulence models and rotating mesh treatment are outside the scope of this paper, but are available at [8]. Free slip conditions were specified at the water surface and no slip conditions were specified at the walls. The near-wall region was modelled via standard semi-empirical logarithmic wall functions. To initialise the model, all velocities were set to zero, whilst k and e were set to 0.001 m2 s2 and 0.01 m2 s3 respectively. For all simulations, the residuals to assess convergence (continuity, velocity components, turbulent kinetic energy, turbulence dissipation rate, specific dissipation rate, and Reynolds stresses, where applicable) were set to 1  105.

Fig. 1. Laboratory scale anaerobic digester.

2.1.3. Mesh density When developing any CFD model, grid density must be optimised such that the key features of the flow field are exhibited, without incurring additional and unnecessary computational expense. In this work, three meshes were constructed containing 278,183, 316,704 and 1,608,169 cells. Grid density analysis was undertaken using the grid convergence index (GCI) method to provide an indication of error bands. [9]. Using the RSM/MRF techniques to simulate the mixing of water in the vessel, velocity magnitude values were extracted for 1000 individual points in the flow field along a vertical line at x = 40, y = 0, 0 < z < 305 mm, and the GCI calculated as:

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J. Bridgeman / Advances in Engineering Software 44 (2012) 54–62

erms GCI ¼ F s 2 r 1 sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 P1000   m¼1 ðum;1  um;2 Þ=um;2 erms ¼ 1000  1=3 h2 r¼ h1

g ¼ K c_ n1 eT 0 =T ð1Þ

where um is the velocity magnitude at point m, h is the number of cells in the mesh, and subscripts 1 and 2 refer to coarse and fine mesh respectively. A factor of safety of 3 (i.e. Fs = 3.0) was applied in accordance with published recommendations [9]. Taking the 278,183 mesh as the baseline, GCIs were calculated for the finer grids as 2.43% (316,704) and 2.12% (1,608,169). The 316,704 cell grid was selected as the model for validation in this study in view of the reduced computational expense compared to the 1,608,169 cell grid and its approximately equivalent performance. A section through the vertical plane of the vessel, showing the grid size and, in particular, the refinement in the impeller regions, is shown in Fig. 2. 2.1.4. Non-Newtonian flow treatment For Newtonian fluids, the viscosity is a function of temperature and pressure only and is the coefficient of proportionality between applied shear stress and velocity gradient. Thus, viscosity is independent of the shear rate. Fluids where this relationship does not hold are classed as non-Newtonian. In the case of non-Newtonian fluids, the viscosity is a function of the shear rate (c_ ) and is termed the apparent viscosity, g.

s g¼ _ c

ð2Þ

Sewage sludge can be considered as a pseudo-plastic (shear thinning) fluid in which viscosity decreases with increasing shear rate. For modelling purposes, the viscosity of shear-thinning fluids may be expressed using a power law.

ð3Þ

where K is the consistency index and n represents the flow behaviour index (n < 1.0 for pseudo-plastic fluids), T0 is the reference temperature and T is the liquid temperature. The power law relationship applies only within a band of applied shear levels and outside of this band, viscosity will take a constant maximum or minimum value, as shown in Fig. 3. Consequently, the modelling approach is to calculate viscosity and, if it falls below the minimum or above the maximum, the maximum or minimum value is adopted as appropriate. For all other cases, the calculated value is used. Rheological characteristics of the sludge were taken from published data [2] and are presented in Table 2. 2.2. Model validation Model validation was undertaken using 2.5% total dry solids (TDS) sludge. Experimental power input measurements were determined from applied torque measurements via

P ¼ 2  p  N  Tq

ð4Þ

where Tq is the applied torque, measured on a torque transducer unit. Using the energy dissipation rate calculated from the turbulence closure model, the overall power consumption was calculated for each mixing speed by numerically integrating the local power consumption over the entire vessel contents, expressed as:

P¼q

Z

edV

ð5Þ

Values for the vessel power consumption were then compared for both the experimental and CFD results using Eqs. (4) and (5). It was concluded from the results (summarised in Table 3) that although the improved fidelity of results gained using the multiple reference frames rotating mesh treatment with the Reynolds Stress

Fig. 3. Shear viscosity as a function of shear rate for a pseudo-plastic fluid.

Table 2 Rheological properties and densities used for sludge modelling (from [2]).

Fig. 2. Mesh density plot.

TS (%)

K (Pa sn)

n

c_ (s1)

gmin (Pa s)

gmax (Pa s)

q (kg m3)

2.5 5.4 7.5 9.1 12.1

0.042 0.192 0.525 1.052 5.885

0.710 0.562 0.533 0.467 0.367

226–702 50–702 11–399 11–156 3–149

0.006 0.01 0.03 0.07 0.25

0.008 0.03 0.17 0.29 2.93

1000.36 1000.78 1001.00 1001.31 1001.73

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J. Bridgeman / Advances in Engineering Software 44 (2012) 54–62 Table 3 Percentage difference between numerically-derived and measured power input data. Scenario

MRF/s k–e

MRF/r k–e

MRF/RNG k–e

MRF/Sk–x

MRF/RSM

Difference in power – experimental vs. CFD data (%) Time to convergence (h)

221 4

17 4

25 4

26 4

13 8

Fig. 4. Mean velocities along central vertical plane for different solids contents. N = 100 rpm in all cases. (a) water, (b) 2.5% TDS, (c) 5.4% TDS, (d) 7.5% TDS, (e) 9.1% TDS, (f) 12.1% TDS.

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J. Bridgeman / Advances in Engineering Software 44 (2012) 54–62

Fig. 5. Modelled trajectories of ten neutrally buoyant particles for different solids contents (water, 5.4%, 9.1% TDS). N = 100 rpm in all cases.

Model (RSM) for turbulence closure (i.e. MRF/RSM) incurred additional computational expense, this was the most appropriate modelling strategy.

3. Results and discussion 3.1. Mean velocity Model mean velocity data were extracted from each 100 rpm mixing scenario. The variation in mean velocity for each solids content along the central vertical plane is shown in Fig. 4a–f. There is a clear reduction in the velocities in vessel with increasing solids content at constant mixing speed. This reduction in velocity is to be expected due to the increased viscosity of the sludge (Table 2) requiring additional energy input to achieve mixing. Thus, maintaining a constant mixing speed (and hence a constant energy input) causes a reduction in velocity within the vessel. However, in-vessel velocities are, of course, not necessarily an indicator of the degree of mixing. The sludge may be moving at a particular speed, but if all sludge in the immediate vicinity is moving at the same speed and in the same direction, then mixing is not occurring, rather the sludge is simply being moved within the vessel en masse. Consequently, the trajectories of particles were assessed within the vessel. Fig. 5 shows the trajectories of 100

massless, neutrally buoyant particles, ‘‘injected’’ into the flow midway between shaft and vessel wall (i.e. r = 0.25D). The figure shows results for water (a), 5.4% TDS sludge (b) and 9.1% TDS sludge (c). It is clear from Fig. 5 that increasing the solids content reduces the ability of particles to move and hence be mixed within the flow field. There is an increasing reduction in the lack of movement of each particle with increasing solids content. However, it is also interesting to note that for the case of particles injected into water, there is still a limitation on the movement of particles, brought about by the competing effects of the two impellers. Effective mixing is an important feature of any digestion facility, not just for the optimisation of the biological processes, but also to prevent deposition of grit and heavier material present in the sludge. Consequently, it is instructive to examine the extent of dead volume within the reactor. Again using 100 rpm as a standard mixing speed, the dead volume was calculated for each mixing speed. In this work, the definition of Vesvikar and Al-Dahhan [6] was adopted, i.e. locations where the velocity is less than 5% of the maximum vessel velocity are considered stagnant or inactive. The results are shown in Fig. 6, and again the effect of increasing solids content on vessel velocity is apparent. When mixing water, the two impellers achieve velocities greater than 5% of the maximum in almost 100% of the vessel. The impellers are also effective at mixing low solids content sludge, as the dead volume is only 1.2% for 2.5% TDS. The effect of increased solids content does

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60

% of total volume

50

y = 0.3053x2 + 0.2469x R2 = 0.989

40

30

20

10

0 0

2

4

6

8

10

12

14

TDS, % Fig. 6. Impact of solids content on dead volume. N = 100 rpm in all cases.

20

% of total volume <5% of max velocity

18 16 14 12 10 8 6

y = 91.733x-0.4971 2 R = 0.9392

4 2 0 0

20

40

60

80 100 120 Mixing Speed, rpm

140

160

180

200

Vol<5% Max Vel Mag Fig. 7. Impact of mixing speed on dead volume for 5.4% TDS sludge.

become apparent, however, when it is increased to 5.4%. This doubling of solids content gives rise to an approximately nine-fold increase in dead volume. Dead volume continues to rise with increasing solids content. It is found that, for the sludges and mixing speed concerned, the relationship between dead volume and solids content can be described effectively by a second order polynomial function, as shown in Fig. 6 (R2 = 0.99). The effect of mixing speed upon dead volume for the same sludge was also considered. Maintaining the solids content at 5.4% (indicative of municipal water sewage sludge), model results were developed for mixing speeds of 30, 50, 100 and 200 rpm. Dead volumes were again assessed on the basis of the 5% of maximum vessel velocity and the results are show in Fig. 7. The data confirm that the reduction in dead volume arising from increased mixing speed can be expressed approximately via a power law equation (R2 = 0.94). An analysis was also undertaken on the proportion of high, medium and low velocities within the vessel at different solids

contents at constant mixing speed. Having considered the full range of velocities across all solids contents mixed at 100 rpm, three velocity bins were assigned; viz. >0.1 m s1 (high velocity zone, HVZ), 0.02 6 velocity 6 0.1 m s1 (medium velocity zone, MVZ), and <0.02 m s1 (low velocity zone, LVZ). For each solids content sludge and water, the proportion of vessel volume in each zone was derived and plotted in Fig. 8. It is apparent from Fig. 8 that the LVZ is almost negligible for the 2.5% sludge, but increases thereafter. There are no LVZ velocities for the water scenario. Of greater interest is the observation that there is little variation in the proportion of volume which experiences high velocities across the range of solids content. The HVZ volume occupancy ranges only from 20.3% to 24.9% (average 23.1%, standard deviation 2.1). The highest velocities are contained within the zones adjacent to the two impellers. Thus, the impellers are able to maintain high velocities in their immediate vicinity and hence the proportion of HVZ volume remains constant. However, as the TDS increases, the impellers have a reducing impact on

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100% 90% 80%

Volume Occupancy

70% 60% 50% 40% 30% 20% 10% 0% 0

2.5

5.4 <0.02 ms-1

7.5 9.1 % TDS 0.02-0.1 ms-1 >0.1 ms-1

12.1

Fig. 8. Change in proportions of high, medium and low velocities with solids content at constant mixing speed (N = 100 rpm).

35

Average velocity gradient, s

-1

30

25

20

15

10

5

0 0

2.5

5.4

7.5

9.1

12.1

TDS, % Bulk

Bottom impeller zone

Top impeller zone

Vessel

Fig. 9. Impact of solids content on average velocity gradient in different zones and in vessel overall. N = 100 rpm.

the more distant bulk vessel contents and so the proportion of LVZ increases, thereby decreasing the proportion of MVZ. 3.2. Velocity gradient By considering the angular distortion of an elemental volume of water when subject to tangential surface forces, Camp and Stein [10] developed the concept of the root mean squared velocity gradient (G) and this has become a fundamental process characteristic within the water industry used to classify mixing vessels. Whilst it is now understood to be flawed in its derivation when considering three-dimensional flows [11,12], and something of an oversimplification in that it attempts to characterise a complex turbulent flow field in one number, the velocity gradient is still used extensively throughout the environmental engineering industry and literature; consequently, an analysis of the velocity gradient distribution in this laboratory digester is appropriate. In this instance, the velocity gradient is defined as:

G¼

rffiffiffi

e g

ð6Þ

where e is the turbulence dissipation rate. For a constant mixing speed of 100 rpm, average G values were extracted from the models and are plotted for the bulk liquid, the impeller regions and the overall vessel average in Fig. 9. A reduction in vessel average values is noticed with increasing solids content from a maximum of 31 s1 for water (0% TDS) to 4 s1 at 7.5% TDS; thereafter the average value remains constant at just 4 s1. For effective anaerobic digestion, literature suggests that the vessel average velocity gradient should be in the range 50–80 s1 [13]. It can be seen that the modelled velocity gradients in this laboratory scale digester are somewhat lower than this range for all solids contents (including water at 0% TDS). The effect of increasing the mixing speed to 200 rpm was assessed numerically, and velocity gradient contours of the vessel midplane section are shown in Fig. 10. It can be seen that even doubling the mixing speed has only

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Fig. 10. Contours of velocity gradient. 5.4% TDS, mixed at 100 and 200 rpm.

14,000

12,000

Volume (ml)

10,000

8,000

6,000

4,000

2,000

0 0

50

100

150 Time (Hours)

Unmixed

200

250

300

100rpm

Fig. 11. Cumulative gas production with time for unmixed and mixed (N = 100 rpm) laboratory digesters.

a slight impact on the turbulent characteristics of the flow field, indicating the inability or inefficiency of the impellers to induce turbulence (and hence mix) sludges with solids content representative of thickened municipal sewage sludge. In order to evaluate the effect of mixing on biogas yield, cumulative gas production was measured in a controlled laboratory experiment over a period of 11 days. 2.5% TDS sludge was digested in four identical anaerobic digesters. One digester was unmixed, one mixed at 20 rpm, one at 60 rpm and one at 100 rpm. The results for the un-

mixed and 100 rpm samples are plotted in Fig. 11. It can be seen that there was no impact on biogas yield from altering mixing speed (similar results were obtained for the 20 and 60 rpm scenarios; data have been omitted for clarity). From Fig. 9 it can be seen that the average G value for 2.5% sludge mixed at 100 rpm is estimated to be 22 s1, approximately 50% of the recommended minimum for effective digestion. Further work is underway to investigate the impact of sludge thickness and mixing on biogas yield. However, it is clear from the combined results of the CFD models and lab scale

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digestion that biogas yield is neither impaired nor improved through mixing of 2.5% TDS sludge in this particular vessel. This is an important observation when considering digester design and optimisation. The current drive is to minimise energy input and maximise biogas yield to develop renewable energy resources. The combination of CFD and experimental data demonstrates an apparent decoupling between mixing energy and biogas yield. This suggests that future designs should focus on reducing the need for energy input for avoidance of grit deposition, rather than optimising mixing energy input from the perspective of biogas yield optimisation. Further work in this project will examine the feasibility of coupling a biogas yield model with CFD models to optimise the complete digestion process and maximise renewable energy production. 4. Conclusions CFD can be used to model effectively the flow fields of a nonNewtonian fluid in a constrained and swirling environment. The effects of increasing solids content of sewage sludge on the mixing characteristics of a laboratory-scale anaerobic digester are significant, and can be demonstrated in terms of velocity magnitude and volume of stagnant zones. The relationship between solids content and stagnant volume can be described effectively by a second order polynomial function. Laboratory scale biogas yield was neither impaired nor improved by changes in mixing speed. Biogas yield can be maintained at velocity gradient values significantly below those recommended in the literature. Further work is required to couple biogas yield models with CFD models in order to optimise gas yield whilst minimising overall energy input. Acknowledgements The computational work reported in this paper was undertaken using the BlueBEAR high performance computing facility at the

University of Birmingham, UK. The author is grateful for the facility and support provided by the University. The laboratory work was undertaken by Mr. Peter Seal and Dr. Cynthia Carliell-Marquet; the contributions of both are gratefully acknowledged. References [1] Bridgeman. Computational fluid dynamics modelling of the mixing of sewage sludge in an anaerobic digester. In: Topping BHV, Costa Neves LF, Barros RC, editors. Proceedings of the twelfth international conference on civil, structural and environmental engineering computing. Civil-Comp Press, Stirlingshire, UK, Paper 260; 2009. doi:10.4203/ccp.91.260. [2] Wu B, Chen S. CFD simulation of non-Newtonian flow in anaerobic digesters. Biotechnol Bioeng 2008;99(3):700–11. [3] Meroney RN. CFD simulation of mechanical draft tube mixing in anaerobic digester tanks. Water Res 2009;43:1040–50. [4] Vera MA, Lavelle P. Digester mixing for scum an grit deposition control. In: 10th European biosolids and biowaste conference, Wakefield, UK; 13–16 November, 2005. [5] Terashima M, Goel R, Komatsu K, Yasui H, Takahashi H, Li YY, et al. CFD simulation of mixing in anaerobic digesters. Bioresour Technol 2009;100: 2228–33. [6] Vesvikar MS, Al-Dahhan M. Flow pattern visualisation in a mimic anaerobic digester using CFD. Biotechnol Bioeng 2005;89(6):719–32. [7] Vesvikar MS, Varma R, Karim K, Al-Dahhan M. Flow pattern visualisation in a mimic anaerobic digester: experimental and computational studies. Water Sci Technol 2005;52(1–2):537–43. [8] Bridgeman J, Jefferson B, Parsons SA. The development and use of CFD models for water treatment flocculators. Adv Eng Software 2010;41:99–109. [9] Roache PJ. Verification of codes and calculations. Am Inst Aeronaut Astronaut J 1998;36(5):696–702. [10] Camp TR, Stein PC. Velocity gradients and internal work in fluid motion. J Boston Soc Civ Eng 1943;30:219–37. [11] Graber SD. A critical review of the use of the G-value (RMS velocity gradient) in environmental engineering. Develop Theoret Appl Mech 1994;17:533–56. [12] Clark MM. Critique of Camp and Stein’s RMS velocity gradient. J Environ Eng 1985;111(6):741–54. [13] Metcalf, Eddy. Wastewater engineering: principles and design. 4th ed. McGraw Hill; 2003.