Anaerobic digestion is a progression of organic procedures in which micro-organisms separate bio-degradable material without oxygen. In this present work, non-Newtonian fluid flow in a mixed-flow anaerobic digester was studied. The flow in the anaerobic digester was simulated in commercially available computational fluid dynamics (CFD) software, ANSYS-Fluent. In this model, numerical simulations were carried out by assuming the liquid in the anaerobic digester to be a non-newtonian fluid. The flow fields in the anaerobic digester are governed by the continuity, momentum, and k-ε standard turbulence equations, and non-Newtonian power law model. To make the comparisons of flow patterns for the Newtonian and the non-Newtonian fluids, several simulations were carried out using a lab-scale cylindrical anaerobic digester. Water and liquid manure with total solid (TS) concentration 2.5% were selected as Newtonian and non-Newtonian fluids respectively. The flow patterns for the Newtonian and the non-Newtonian fluids were completely different. To characterize the flow fields with respect to the rheological properties of liquid manure, comprehensive flow simulations were carried out at four TS levels (TS 0%, 2.5%, 7.5%, and 12.1%) with pump power input 0.5 HP in 3-D anaerobic digester. The results indicate that at the higher TS the mixing quality is poor at the same power input. The optimum power input for a cylindrical digester with volume of 1 m3 and inlet pipe with r = 0.05 m was determined and found that 0.375 HP is the optimal power input in this case.
Keywords: Anaerobic Digester; Total Solid Concentration; Non-Newtonian Fluid; CFD; Sludge Rheology;
Anaerobic digestion is a system in which sequence of biological processes take place to break down organic materials and produce biogas in the absence of oxygen. The rate of energy consumption of the world is increasing significantly day by day. The worry of feasible power sources and the impact of fossil fuel emissions push the nations around the globe to discover variant power source . Nuclear power and sustainable power source are the world’s quickest developing power sources. Biogas is one of the vitality sources sorted as sustainable power source. One of the final results of anaerobic digestion is biogas. This procedure may be used for human benefits by controlling the procedure in wastewater treatment and other facilities. Industrial and metropolitan wastewater may be dealt with anaerobically relying upon the substrate enclosed in it . Mixing plays vital role for efficient anaerobic digestion. Anaerobic reactor design and advancement may be done by using the modelling as input . With the help of simulation and modelling tools biogas production may be maximized . Depending on the total solids, temperature and other factors, organic materials such as livestock manure, animal waste, and industrial waste slurries exhibit non-Newtonian behavior . In this model, numerical simulations were carried out by assuming the liquid in the anaerobic digester to be a non-newtonian fluid. Over the last few era, anaerobic digestion procedure was described based on the endless empirical, mechanistic, mathematical models .
Anaerobic digester has a long history, it was first introduced in Assyria at the time tenth century BCE, where shower water was heated by using biogas . During 17th century, Boyle and Hales noticed that irritating the residue of streams and lakes discharged combustible gas. From then scientific interest was shown for the generation of gas by using the biological decomposition of organic substance. Scientifically, the gas was identified as methane in 1778 by the Italian physicist Alessandro Volta, who is recognized as the father of Electrochemistry . In India, in 1859, anaerobic digester was constructed which the first ever built. In England, the innovation was created in 1895, by which gas was produced by utilizing a septic tank. For sort of gas lighting, the sewer gas destructor light used the gas. In 1905, in Hamton, London, the dual-purpose tank for both sludge treatment and deposition was built . At the beginning of the twentieth century, anaerobic assimilation methods started to look like the innovation as it shows up today. Imhoff made the Imhoff tank in 1906 which was an early type of anaerobic digester and it was usually used for the treatment of wastewater at that time . The closed tank methods started to supplant the beforehand regular utilization of anaerobic tidal ponds secured earthen bowls used to treat unstable solids in 1920. During the 1930s, analysis on anaerobic metabolism started vigorously . Sufficient mixing gives a uniform situation to anaerobic microscopic organisms, which is one of the central points in acquiring greatest digestion. Inefficient mixing may diminish the viable volume of a digester by as much as 70%, leaving a genuine volume use of just 30% . A dynamic model was utilized to research the impacts of imperfect mixing on anaerobic reactors for sewage sludge treatment . A 3-D flow model was developed to enhance the economy and efficiency of covered anaerobic reactor systems including bulk fluid motion, sedimentation, buoyant mixing, bubble mixing, bubble entrainment, biological reactions by Fleming . Modified pilot-scale anaerobic digesters with mixing pit and baffling configurations showed best hydrodynamic characteristics . A mathematical model of non-ideally mixed continuous flow reactors was developed by Keshtkar for anaerobic digestion of cattle manure . The flow patterns were identified and different hydrodynamic parameters ware obtained in mimic anaerobic digester performing three-dimensional steady state CFD simulations by Al-Dahhan and Vesvikar . The sparging gas provides the appropriate mixing in the anaerobic digesters at three diverse stream rates. Air was used as gas stage and water was used as liquid stage for the simulation . For the optimal design and less expensive operation and regulation of anaerobic digester, the nature of the organic sludge and rheological properties play important role according to O’Neil . Non-Newtonian characteristics are displayed by most of the organic materials which is firmly subject to absolute solids, temperature, bioprocess and different elements . Moilanen, Laakkonen & Aittamaa  expressed that stock rheology exhibits behavior like water at first, then yet regularly ends up thick and toward the end becomes non-Newtonian. Achkari-Begdouri & R. Goodrich  analyzed animal compost slurry and he showed that the animal compost slurry exhibits non-Newtonian behavior to the extent compost properties are concerned. Achkari-Begdouri & R. Goodrich  examined the rheological characteristics of Moroccan farm cattle compost then he inferred that the compost acts like a pseudo-plastic suspension liquid at temperatures somewhere in the scope of 20 and 60ºC when total solid concentration between 2.5 to 12.1%. Landry, Laguë, & Roberge  estimated the physical and stream characteristics of compost items at different total solid concentration, and finally displayed the polynomial relapse conditions for ascertaining the mass thickness and evident consistency of dairy cows, poultry, sheep and pig excrement. El-Mashad, Loon, Zeeman, & Bot  studied the Rheological properties of dairy cattle manure, and estimated the consistency of fluid excrement with total solid concentration 10% at various shear rates. The outcomes demonstrated that excrement has non-Newtonian stream characteristics and acts like genuine plastic materials. The above discussion investigations were just constrained to compost’s physical and rheological properties without implementing them to blending investigation. Wu and Chen  first brought non-Newtonian liquid hypothesis into anaerobic digester. Sajjadi et al.  studied non-Newtonian flow behavior of municipal sludge in anaerobic digesters using submerged, recirculating jets. Wu  investigated mixing in egg-shaped anaerobic digesters. Conti et al.  studied various geometric configurations to determine efficient mixing quality and disclosed that configurations with the rotors far away from the bottom and high rotational angles cause beneficial to fluid dynamics. Meister et al.  investigates the non-Newtonian flow in impeller induced mechanical draft tube. Tobo et al.  analyzed partial integration of Anaerobic Digestion Model no. 1 (ADM1) into the CFD model and investigated the effect of advection–diffusion transport on anaerobic digestion mixing.
There are three types flow, namely laminar, transition and turbulent depending on the transport quantities such as mass, momentum and energy. When all the transport quantities show sporadic changes in time and space, the flow is called turbulent. Wu investigated different turbulence models in anaerobic digesters  and showed, as quoted by Craig , that most digester flow are turbulent. There are different types of turbulence models such as Large Eddy Simulation (LES), Reynolds Averaged Navier-Stokes (RANS), Shear Stress Transport (SST), Standard k-ε. However, in this research work Standard k-ε turbulence model has been used.
In this study, two types anaerobic digester were used for the simulation, one is 2-D for comparing the flow patterns between the Newtonian and non-Newtonian fluid and the other is 3-D for the evaluation of the effect of rheological properties in the flow fields. At first, the lab-scale digester model  was used to simulate the mixing in order to validate the model. Then, for investigating the effect of total concentrations, a cylindrical digester was used and investigated the variation of velocity with respect to the total solid concentrations. Finally, optimal power input was determined for specific cylindrical digester.
The remaining of the paper contained a short description of theoretical methodology in the first section. In the second section, numerical methodology is described and geometric configurations are constructed. In the next section, simulations and results are displayed and analyzed. Finally, findings of the work are presented in conclusions section.
Mass conservation, momentum conservation and transport of turbulence are the key factors to define the mixing flow model in an anaerobic digester. The temperature of the fluid slurries in the flow field may change to develop reasonable environment for producing bacteria. The fluid flow may be steady or transient depending on the phase change of liquid manure during biogas production . The nature of fluid may be Newtonian or non-Newtonian depending on the total solid concentration in the liquid. Therefore, in an anaerobic digester, the mixing flow fields is very complex when all the parameters are considered. In this case the flow simulation will be very difficult and expensive. Therefore, in building up a hypothetical model, the following assumptions were made:
- Liquid flow is considered as steady and 3-D in the digester.
- Fluid is non-Newtonian fluid.
- Fluid is incompressible.
- The temperature of the fluid is constant.
- There is no heat transfer in the flow model as the temperature of the liquid manure is considered as constant at 35ºC.
- The model is limited to single stage. So, the bubble-fluid stage communication is unimportant.
The flow in the digester is governed by the mass and momentum transport equations. Mass conservation equation is given by ,
where ρ is fluid manure density and µi is fluid velocity in tensor form
Momentum conservation is expressed as ,
where p is static pressure, τij stress tensor and ρgi gravitational force in the i direction.
The stress tensor, τij , is expressed by ,
where µ is molecular viscosity.
When mass, momentum and energy show occasional, sporadic changes in reality, the flow is called turbulent. Turbulent model varies depending on the different flow conditions . ANSYS Fluent gives a wide assortment of models depending on the nature of different problems. Required dimension of exactness and the accessible CFD assets play important role for selecting the turbulent model. In this research work, the standard k-ε turbulence model, which is developed by Launder and Spalding , has been used for the simulation.
For turbulent kinetic energy k:
For dissipation rate ε
Where Gk , is the turbulence kinetic energy for the average velocity gradients. Gb is turbulence kinetic energy for buoyancy. C1e , C2e and C3e are constants. σk represents Prandtl number for k and σε represents the Prandtl number ε.
The turbulent viscosity µt is computed by combining k and ε as follows:where Cµ is a constant.
The model constants C1ε , C2ε , C3ε , σk and σε have fixed values such as C1ε = 1.44, C 2ε= 1.92, C3ε = 0.09, σk = 1.0, σε = 1.3 .
Non-Newtonian Fluid Model
Fluids are classified into two types based on the Newton’s law of viscosity. Newtonian fluids follow the Newton’s law of viscosity. A Newtonian fluid is defined as the fluid in which the ratio of the viscous stress to the strain rate is constant. On the other hand, nonNewtonian fluid does not follow the Newton’s law of viscosity. In this case, the linear relation is not valid. In non-Newtonian fluids, viscosity can change when under force to either more liquid or more solid. Most commonly, the viscosity of non-Newtonian fluids is dependent on shear rate . The fluid can even exhibit timedependent viscosity.
In case of non-Newtonian fluids, the shear stress, , may be defined in terms of non-Newtonian viscosity as :
where η represents non-Newtonian viscosity.
As the shear rate is increased, the liquid manure sludge usually shows a decreasing viscosity, which is the characteristics of the pseudo-plastic fluids. Non-Newtonian power law viscosity is defined as :
where γ represents shear rate (s-1), K represents consistency coefficient (Pa sn ), n means the power-law index, T represents the liquid manure temperature (K) and To means the reference temperature (K). When n< 1, the fluid is pseudo-plastics; for Newtonian fluid n=1 and for n>1 , the fluid is dilatant.
The power law model requires the computation of the lower and upper limits of viscosities (ηmin and ηmax). If the computed viscosity is less than ηmin , the value of ηmin will be used instead. Similarly, if the computed viscosity is greater than ηmax, the value of ηmax will be used instead.
The liquid manure bulk density (ρ) proposed by Landry et al. ,
where TS is weight percentage of total solid in liquid manure
The flow behaviors of Newtonian and non-Newtonian fluids are not same. So, the Reynolds number of non-Newtonian fluids is different from the Newtonian fluids. Reynolds number for nonNewtonian fluid proposed by Metzner and Reed ,
Where U∞ represents the mean velocity of the liquid manure (m/s) and D means inside diameter (m) of the pipe.
Computational fluid dynamics consists different type of steps and these steps must be solved sequentially. Usually the solution of computational fluid dynamics is categorized into three steps such as pre-processing, solution and post-processing. Pre-processing consists of geometrical model, mesh generation and defining boundary conditions. All the processes are described below.
In pre-processing step geometrical model of the domain of interest is generated. Then the model is discretized into number of finite volumes which is known as meshing. Finally, initial and boundary conditions are defined into the geometry.
The initial step is to construct a geometrical model for the area of intrigue. By and large, the real geometry consists of a great deal of fine parts, due to this the mesh generated may be very complicated with numerous components. So, the geometrical model is generally simplified in order to avoid meshing difficulties but this may cause some error in the result.
The greater part of the digester geometries executed for computational fluid dynamics demonstrating include a tubeshaped tank in which mixing is done by means of mechanical and gas lifting. Different areas have been considered, for example, flat pipes and egg-formed digesters. But in this research cylindrical digester reactor was chosen.
In this work two geometries of anaerobic digester have been used for the simulation, one is 2-D and other 3-D. 2-D digester was used for comparing the flow patterns between Newtonian and nonNewtonian fluid. The geometric model of the 2-D digester is shown and dimensional specifications are shown in Figure 1.
Figure- 1: Geometrical model (left) and dimensional specifications (right) of the 2-D anaerobic digester
Figure 2 (left) shows the geometrical model of 3-D anaerobic digester which specially was used for the evaluation of the effect of rheological properties in the flow fields at different TS on the non-Newtonian fluids. It was also used for the determination of the optimum power input of the anaerobic digester at different power input. The right of Figure 2 shows the specifications of the geometrical model of 3-D anaerobic digester in 2-D form. The volume of this cylindrical digester is approximately 1 m3.
Figure 2: Geometrical model (left) and dimensional specifications (right) of the 3-D anaerobic digester
In mesh generation step, the geometrical model is discretized into various finite elements or volumes according to the computational fluid dynamics method. In this research the solution was discretized into a number of finite volumes since the ANSYS Fluent uses the finite volume method.
Figure 3 (left) shows the mesh generated in the 2-D anaerobic digester model. The elements of the mesh were increased by face sizing. Most of the grids generated are structural and some are unstructured. The right of Figure 3 shows the mesh generated in the 3-D anaerobic digester model. The elements of the mesh were increased by face sizing. The grids generated in this digester are unstructured.
Figure 3: Generated mesh pictures in the 2-D (left) and 3-D (right) models of anaerobic digester geometry
After meshing the geometry, the boundary conditions are set by defining the inlet flow as “velocity inlet” at the predetermined esteem, and the outlet flow as “pressure outlet”. The other faces named as wall and were subjected to no slip condition.
Now in the solution step solvers are chosen, turbulence models are selected, convergence criteria are defined and the materials are chosen. The solver delivers the result at the predefined grid elements. A solver may be specified in different ways depending on the type of problem. Determination of the right solver apparatus is frequently significant in creating an important result. In this research work, the solver was defined as steady state, and pressure based to solve the flow equations (momentum and continuity).
The solution method for this simulation was set as:
- Pressure-velocity coupling scheme to Coupled
- Gradient to Least squares cell based
- Pressure to Second order
- Momentum to Second order upwind
- Turbulent kinetic energy to First order upwind
- Turbulent dissipation rate to First order upwind
In order to make non-Newtonian fluid in the ANSYS Fluent, rheological properties of the fluid has to be defined by activating the non-Newtonian power law model by writing text command in the Fluent. Before writing text command in the Fluent, the turbulent model must be activated otherwise the non-Newtonian power law model will not activate. The text command is given below .
After writing the above text command and pressing the “enter” key the following command will be appeared in the screen:
Enable turbulence for non-Newtonian fluids? [no]
Then type “yes” in the text command.
Total solid concentration controls the rheological properties of fluid. In this thesis work, rheological properties and densities of non-Newtonian fluid were taken from Achkari et al.  and Landry et al.  as displayed in Table 1. Here, n represents powerlaw index, K represents consistency coefficient, γ represents shear rate, ηmin represents minimum viscosity, ηmax represents maximum viscosity and represents densit y of fluid. Minimum and maximum viscosities are determined from equation (7). When total solid (TS) concentration is 2.5%, ηmin = 0.006 Pa s for γ = 702 s-1 and ηmax = 0.008 Pa s for γ = 226 s-1 were respectively determined. Table:1
Table 1: Rheological properties and densities of fluid manure for T = 35ºC( , )
K (Pa sn)
ηmin (Pa s)
Results and Discussion
Grid Independence Test
A mesh independence test was carried out for the computational domain for improving the accuracy of the simulations. For the Newtonian fluid at 2 m/s velocity of inlet, the average velocity in the digester was determined for the different mesh elements. The variation of result with respect to the mesh element is shown in Figure 4 below. From the figure it can be observed that average velocity is nearly constant around mesh elements 2654 to 5051. So, simulation was carried out by setting the mesh elements 4711.
Figure 4: Variation of average velocity with respect to the number of elements
Figure 5: Velocity contours of Newtonian fluid when velocity of inlet is 2 m/s (a) paper work (b) present work
The above Figure 5 shows the contours of velocity magnitude of Newtonian fluid with inlet velocity 2 m/s for paper work and present work. From the figure it can be observed that the flow path for Newtonian liquid is along the right side wall and afterwards towards the outlet for both paper work and present work.
Figure 6: Velocity contours of non-Newtonian fluid when velocity of inlet is 2 m/s (a) paper work (b) present work
The above Figure 6 shows the contours of velocity magnitude of non-Newtonian fluid with inlet velocity 2 m/s for paper work and present work. It can be observed that the flow patterns of non-Newtonian liquid are along the left side wall and afterwards towards the outlet for both paper work and present work. So, both the Newtonian and non-Newtonian fluid simulation agree with the paper work
Identification of Flow Patterns
In this research work, to compare the flow patterns between Newtonian liquid and non-Newtonian liquid, different numerical simulations were done utilizing 2-D anaerobic digester model. Water was selected as Newtonian fluid. The density of water is 1,000 kg/m3 , and the water viscosity is 0.001003 Pa s. Liquid manure with TS (total solid) 2.5% were selected as non-Newtonian fluid. The liquid manure density is 1000.36 kg/m3 and the minimum viscosity of liquid is 0.006 Pa s and maximum viscosity is 0.008 Pa s. The consistency coefficient K is 0.042 Pa sn and power law index n is 0.71.
Figure 7shows the contours of velocity magnitude of Newtonian liquid and non-Newtonian liquid at inlet velocity 2 m/s. From the Figure 1, it can be observed that the flow for the Newtonian liquid is along the right side wall and then reaches the outlet. In case of the non-Newtonian liquid the flow patterns are along the left side wall.
Figure 7: Velocity contours of Newtonian and non-Newtonian liquid when the velocity of inlet is 2 m/s.
(a) Newtonian liquid, (b) Non-Newtonian liquid
Figure 8: Velocity contours of Newtonian and non-Newtonian liquid when velocity of inlet is 5 m/s.
At inlet velocity of 5 m/s the above Figure 8 shows the contours of velocity magnitude of Newtonian liquid and non-Newtonian liquid. From the above figure, it can be observed that when the velocity magnitude increased from the inlet flow velocity 2 m/s to 5 m/s, the general flow patterns remain unaltered.
Effect of Rheological Properties in the Flow Fields
In this study, so as to describe the flow fields as for the rheological properties of fluid slurry, various numerical simulations were done at four total solid (TS) concentration (TS 0%, 2.5%, 7.5%, and 12.1%) for a pump power input 0.5 HP (i.e. inlet velocity 3.8 m/s) in the digester of 1 m3 volume. Figure 9 below demonstrates volume percentage of digester according to the velocity zones at four TS levels for power input 0.5 HP.
To quantify the flow fields, three velocity zones were defined as low velocity zone (0 < v ≤0.05 m/s), medium velocity zone (m/s), and high velocity zone (m/s), respectively. From the figure, it can be observed that when the total solid concentrations in the liquid increase then the low velocity zones increase but the medium velocity zones decrease. The effects of total solid in the high velocity zones are insignificant. So, at the higher TS the mixing quality is poor at the same input power
Figure 9: Volume percentage of digester according to the velocity zones at four TS levels for power input 0.5 HP. .
Determination of Optimum Power Input
In this study, in order to determine optimum power input, an anaerobic digester of volume 1 m3 is selected. In this case, flow simulations were carried out at four pump power input (0.125, 0.25, 0.375, 0.5 HP).
The hypothetical input power of the pump can be determined by the equation 
where ρ represents fluid density, g is the gravity (9.81 m/s2 ), H is the liquid hydrostatic head (m), and Q is the flow rate of fluid (m3 /s).
Velocity of inlet of the anaerobic digester can be calculated from the Equation (11) when the pump power is known such as when the power is 0.125 HP, the velocity of inlet is 1 m/s. Fig. 4 below demonstrates percentage of velocity of different velocity zone altering with the various power input when total solid concentration is 12.1%. From the Figure 10 it can be observed that the percentage of velocity decrease when v< 0.01 m/s and percentage of velocity increases when v>0.01 m/s as the input power increases. It is also clear that most velocity zones are in the range of 0.001 and 0.5 m/s velocity. At the time input power is 0.375 HP, the velocity curves slopes are nearly zero. According to the logic of mathematics, this point is the critical or extreme point since at this point the value of slope is zero. The numerical simulation objective is to locate the extreme point. So, it may be deduced that in this scenario 0.375 HP is the ideal input power.
Figure 10: Velocity zones VS power input at TS 12.1%
In this study, numerical modelling of non-Newtonian fluid flow in anaerobic digesters was analyzed. CFD software ANSYS Fluent was used to simulate the different flow field in the anaerobic digester. Non-Newtonian liquid was created by activating non-Newtonian power-law in the Fluent. Non-Newtonian liquid properties are taken from the literature. From the numerical simulation of flow fields in the digesters, the following facts may be concluded:
- The flow patterns are not same between Newtonian liquid and non-Newtonian liquid flow in the anaerobic digester.
- When the velocity in the inlet is increased from 2 m/s to 5 m/s, the flow patterns remain unchanged in the digester. So, the velocity magnitude can not change the flow patterns.
- At the same power input, the mixing quality is poor at the higher total solid concentration. The low velocity zone increases when the total solid concentrations increase in the liquid but high velocity zones remain unchanged.
- For cylindrical anaerobic digester with volume 1 m3, the velocity curve slope is nearly zero. So, 0.375 HP is the optimum power input.
In this work, the effect of temperature variation of the liquid manure was neglected. In the future work, it can be considered. The model was assumed single phase. In the future the bubble-liquid phase interaction may be considered. The organic procedure has been neglected while assessing the performance of the digester. In future work, organic process may be evaluated.
A - area, m2
CFD - computational fluid dynamics
D - diameter, m
g - gravity, m/s2
G - generation of turbulent kinetic energy, J/m3 s
h - vertical distance, m
H - hydrostatic head, m
H - height, m
HP - Horse powers
k - turbulent kinetic energy, m2 /s2
k - consistency coefficient, Pa sn
L - length, m
n - power-law index
p - pressure, N/m2
p - power, HP or W
Q - volumetric flow rate, m3/s
r - radius of inlet or outlet pipe, m
R - radius of digester, m
Re - reynolds number, dimensionless
t - time, s
T - temperature, K or ºC
TS - total solid concentration, g/L
u - velocity magnitude, m/s
U - velocity magnitude, m/s
v - velocity magnitude, m/s
V - digester volume, m3
ρ - density, kg/m3
𝜏 - ar stress, Pa
ε - dissipation rate of turbulent kinetic energy, m2/s3
µ - dynamic viscosity, Pa s
η -non-Newtonian viscosity, Pa s
σ - turbulent Prandtl number, dimensionless
γ - shear rate, s-1
i,j - tensor form
x - coordinate
The authors are grateful to the Khulna University of Engineering & Technology for sponsoring this research and CFD lab of the Department of Mechanical Engineering of this university for providing facilities for the simulations.
- Global Environment Outlook 3: past, present and future perspectives. United Nations Environment Programme. London. 2002.
- J Brigdeman. Computational fluid dynamics modelling of sewage sludge mixing in an anaerobic digester. Advances in Engineering Software. 2012;44:54-62.
- Sadino-Riquelmea C, Hayes RE, D. Jeisonb and A. Donoso-Bravo. Computational fluid dynamic (CFD) modelling in anaerobic digestion: General application and recent advances. Critical Reviews in Environmental Science and Technology. 2018;1-48:39-76.
- Singh B, SzamosiZ and Simenfalvi Z. State of the art on mixing in an anaerobic digester: A review. Renewable Energy. 2019;141:922-936.
- D J O'Neil. Rheology and mass/heat transfer aspects of anaerobic reactor design. Biomass. 1985;8(3):205-216.
- Donoso-Bravo A, Mailier J, Martin C, Rodriguez J, Aceves-Lara CA and AV Wouwer. Model selection, identification and validation in anaerobic digestion: a review," Water Research. 2011;45(17):5347-5364.
- Auer A, Burgt NHV, Abram F, Barry G, Fenton O, Markey BK and et al. Agricultural anaerobic digestion power plants in Ireland and Germany: policy and practice. Journal of the Science of Food and Agriculture.2017;97(3):719-723.
- Gijzen H. Anaerobic digestion for sustainable development: a natural approach. Water Sci Technol. 2002;45(10):321-328.
- Marsh G. Rise of the Anaerobic Digester. Renewable Energy Focus. 2008;9(6):28-30,32,34.
- Grando RL, Antune MDS, Fonseca FV, Sanchez A, Barrena R and Font X. Technology overview of biogas production in anaerobic digestion plants: A European evaluation of research and development. Renewable and Sustainable Energy Reviews. 2017;80:44-53.
- Edwards J, Othman M and Burn S. A review of policy drivers and barriers for the use of anaerobic digestion in Europe, the United States and Australia. Renewable and Sustainable energy Reviews. 2015;52:815-828.
- Monteith HD and Stephenson JP. Mixing efficiencies in full-scale anaerobic digesters by tracer methods. Journal (Water Pollution Control Federation). 1981;53:78-84.
- Bello-Mendoza R and Sharratt PN. Modelling the effects of imperfect mixing on the performance of anaerobic reactors for sewage sludge treatment. Journal of Chemical Technology &Biotechnology. 1998;71(2):121-130.
- Fleming JG. Novel simulation of anaerobic digestion using computational fluid dynamics. North Carolina state University. Raleigh, NC. 2002.
- Pena M, Mara D and Piguet JM. Improvement of mixing patterns in pilot-scale anaerobic pond treating domestic sewage. Water Science and Technology. 2003;48(2):235-242.
- Keshtkar A, Meyssami B, Abolhamd G, Ghaforian H and Asadi MK. Mathematical modeling of non-ideal mixing continuous flow reactors for anaerobic digestion of cattle manure. Bioresource Technology. 2003; 87(1):113-124.
- Vesvikar MS and Al-Dahhan M. Flow pattern visualization in a mimic anaerobic digester using CFD. Biotechnology and Bioengineering. 2005;86(6):719-732.
- Moilanen P, Laakkonen M and Aittamaa J. Modeling aerated fermenters with computational fluid dynamics. Ind. Eng. Chem. Res. 2006;45(25):8656-8663.
- Achkari-Begdouri A and Goodrich PR. Rheological properties of Moroccan dairy cattle manure. Bioresource Technology. 1992;40(2):149-156.
- Landry H, C. Lague C and Roberge M. Physical and rheological properties of manure products. Applied Engineering in Agriculture.2004;20(3):277-288.
- El-Mashad HM, W KP v. Loon, Zeeman G and G P A Bot. Rheological properties of dairy cattle manure. Bioresource Technology. 2005;96(5):531-335.
- Wu B and Chen S. CFD Simulation of Non-Newtonian Fluid Flow in Anaerobic Digesters. Biotechnology and Bioengineering. 2008;99(3):700-711.
- Sajjadi B, Aziz A, Raman A and Parthasarathy R. Fluid dynamic analysis of non-Newtonian flow behavior of municipal sludge simulant in anaerobic digesters using submerged, recirculating jets. Chemical Engineering Journal. 2016;298:259-270.
- Wu B. CFD simulation of mixing in egg-shaped anaerobic digesters. 2010;44:1507-1519.
- Conti F, Saidi A and Goldbrunner M. CFD Modelling of Biomass Mixing in Anaerobic Digesters of Biogas Plants. Environmental and Climate Technologies. 2019;23(3):57-69.
- Meister M, Rezavand M, Ebner C, PümpelTand, Rauch W. Mixing non-Newtonian flows in anaerobic digesters by impellers and pumped recirculation. Advances in Engineering Software. 2018;115:194-203.
- Tobo YM, Rehman U, Bartacek J and Nopens I. Partial integration of ADM1 into CFD: understanding the impact of diffusion on anaerobic digestion mixing. Water Science & Technology. 2020.
- Wu B. CFD investigation of turbulence models for mechanical agitation of non-Newtonian fluids in anaerobic digesters. Water Research. 2011;45(5):2082-2094.
- Craig K, NieuwoudtM and Niemand L. CFD Simulation of Anaerobic Digester with Variable Sewage Sludge Rheology. Journal of Water Research. 2013;47(13):4485-4497.
- Chen J, Chen A, Shaw J and Yeh C. CFD Simulation of Two-Phase Flows in Anaerobic Digester. Journal of Physics: Conference Series. 2019.
- Potter MC, Wiggert DC, Ramadan B and Shih TIP. Mechanics of Fluids, 4th Edition. Global Engineering: Christopher M. Shortt. 2012.
- Launder BE and Spalding DB. Lectures in mathematical models. London. Academic Press, England. 1972.
- MetznerAB and Reed JC. Flow of non-Newtonian fluids-correlation of laminar, transition and turbulent-flow regions. AIChE Journal. 1955;1(4):434-440.
- ChhabraR and Richardson J. Non-newtonian flow in the process industries: fundamentals and engineering applications. Butterworth-Heinemann. 1999.
- Modi PN and Seth SM. Hydraulics and Fluid Mechanics Including Hydraulic Machines, 4th edition. Delhi: Rajinder Kumar Jain; Standard Book House. 2002.