# CFD Modeling of a Stirred Anaerobic Digestion Tank for Evaluating Energy Consumption through Mixing

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Geometry and Meshing

#### 2.2. Assumptions

- Since the flow enters the digester for just 15 min during a six-hour period, the effect of the inlet and outlet flow is not significant.
- 2 m of the tank is filled by the feedstock.
- The shear-thinning non-Newtonian characteristics of the feedstock are considered.
- The density of the fluid is constant and calculated as 1001.7 kg/m
^{3}, based on [30]. - The effect of temperature is assumed as constant.

#### 2.3. CFD Method

#### 2.4. Equations

#### 2.5. Physical Characteristics

#### 2.6. Boundary and Zone Conditions

## 3. Results and Discussion

#### 3.1. Validation

#### 3.2. Grid Independence

_{1}, φ

_{2}, and φ

_{3}denote the velocity magnitude at the mentioned point for the cases with 101,894, 222,058, and 462,912 elements, respectively (see Table 3). The variable φ

_{ij}abbreviates φ

_{j}− φ

_{i}, and the ratios of the grid refinement are shown by r

_{21}and r

_{32}. Then the order of convergence (p) is determined by iteratively solving the 11th equation in [26]. By calculating the relative error between the two finest meshes (e

_{32}$=\left|\frac{{\phi}_{32}}{{\phi}_{2}}\right|$), the GCI value, with a safety factor of 1.25, is calculated as almost equal to 0.02%. It was, thus, concluded that the model with 222,058 elements is suitable for the simulation.

#### 3.3. Contours and Vectors

#### 3.4. Data Analysis

^{3}or 0.47% of the volume, respectively.

^{3}) to 0.47% (1.66 m

^{3}), respectively. This shows an increase of about 133%, which can be considered as a significant variation in the total volume of dead zones, although all of the obtained values for the dead volume are negligible as compared to the total volume of the fluid. It is concluded that by increasing the TS concentration, the volume of dead zones increases.

^{−1}. In this research, G is determined by post-processing of the achieved data (utilizing volume integrals in the software) as 26 s

^{−1}. Thus, mixing does not avoid formation of the sedimentation layer and an additional sewage pump regime is necessary to improve the performance of the AD. A solution could be reducing the amount of the mixer rotation speed; however, due to structural limitations, reducing the mixing speed is not possible in our case.

^{3}. While this is still only about 0.73% of the digester volume, we denote that the effect is obviously contrary to the intended one (a 36% increase in the amount of dead volume as compared to the case where the mixer is at the central height). For both the velocity gradient and the power consumption, no significant difference is found for this scenario.

^{3}for a rotation speed of 300 rpm to 0.12 m

^{3}for a rotation speed of 500 rpm. In general, the dead volume decreases as the mixer rotation speed increases, but the relation is non-linear. This is different for the velocity gradient as this value increases from 26 s

^{−1}for the mixer with the rotation speed of 300 rpm to 56.5 s

^{−1}for the mixer with the rotation speed of 500 rpm. As the minimum mixer rotation speed (300 rpm) already leads to higher values in velocity gradient, increasing the speed does not help in keeping the G value in its optimum range. Moreover, when the mixer rotates with the speed of 500 rpm, the power consumption increases to about 159.9 kW (according to Equation 5), which is quite high for such a plant size. Indeed, the amount of power consumption at 500 rpm is more than six times the one required for 300 rpm. For different mixer rotation speeds, the power consumption is summarized in Table 4.

## 4. Conclusions

- The dead zone was found near the central column and the walls of the digester because the applied mixer mostly affects the regions located at the same height and radial distance as the mixer.
- Power consumption increases by increasing TS concentrations, especially at higher TS concentrations. Similarly, by increasing TS concentrations, the amount of dead volume increases considerably.
- There is not a huge change for dead volume once the mixer rotation speed increases to 400 rpm and higher, while the energy needed for mixing increases.
- It is not recommended to increase the mixer rotation speed to more than 300 rpm, since—besides the deteriorative effect of the higher velocity gradient—the energy consumption of the mixer increases.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**The location of the digester tank (

**a**), the internal view of digester tank including its mixer (

**b**), designed geometry to simulate agitation inside the tank (

**c**), mesh implementation for the tank and mixer zones (

**d**).

**Figure 2.**Velocity profiles along the vertical line within the digester for the meshes with 101,894, 222,058, and 462,912 elements.

**Figure 3.**Velocity contours of the three horizontal planes, located at the heights of 0.5 m (

**a**), 1 m (

**b**), and 1.5 m (

**c**) from the floor of the digester; and velocity contours of two vertical planes (

**d**,

**e**) in the digester.

**Figure 4.**Streamlines derived from three horizontal planes situated at the heights of 0.5 m (

**a**), 1 m (

**b**), and 1.5 m (

**c**) from the floor.

**Figure 5.**Velocity vectors mapped in the three horizontal planes situated at the heights of 0.5 m (

**a**), 1 m (

**b**), and 1.5 m (

**c**) from the floor, and the two vertical planes located according to Figure 3 (

**d**,

**e**).

**Figure 7.**The location of each horizontal plane (

**a**), and the plot of the average velocity at each horizontal plane at its corresponding height (

**b**).

**Figure 8.**The created dead volume and power consumption for each TS concentration within the feedstock.

**Table 1.**Rheological properties used for sludge modeling (from [38]).

$\mathit{T}\mathit{S}\left(\mathit{\%}\right)$ | $\mathit{K}\left(\mathit{P}\mathit{a}{\mathit{s}}^{\mathit{n}}\right)$ | $\mathit{n}$ | $\dot{\mathit{\gamma}}\left({\mathit{s}}^{-1}\right)$ | ${\mathit{\eta}}_{\mathit{m}\mathit{i}\mathit{n}}\left(\mathit{P}\mathit{a}\mathit{s}\right)$ | ${\mathit{\eta}}_{\mathit{m}\mathit{a}\mathit{x}}\left(\mathit{P}\mathit{a}\mathit{s}\right)$ |
---|---|---|---|---|---|

12.1 | 5.885 | 0.367 | 3–149 | 0.25 | 2.93 |

Boundary | Type | Characteristic |
---|---|---|

Lateral walls | Wall | No-slip shear condition |

Mixer impellers | ||

Central column walls | ||

Upper surface | ||

Lower surface |

Parameter | Unit | Value |
---|---|---|

φ_{1} | m/s | 0.4907 |

φ_{2} | 0.4846 | |

φ_{3} | 0.4839 | |

| φ_{21}| | m/s | 0.0061 |

| φ_{32}| | 0.0007 | |

r_{21} | - | ≈1.3 |

r_{32} | ≈1.3 | |

p | - | 8.24 |

e_{32} | % | 0.14 |

Mixer Rotation Speed (rpm) | Power Consumption (kW) |
---|---|

300 | 24.5 |

350 | 47.1 |

400 | 78.4 |

450 | 117.6 |

500 | 159.9 |

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**MDPI and ACS Style**

Dabiri, S.; Noorpoor, A.; Arfaee, M.; Kumar, P.; Rauch, W.
CFD Modeling of a Stirred Anaerobic Digestion Tank for Evaluating Energy Consumption through Mixing. *Water* **2021**, *13*, 1629.
https://doi.org/10.3390/w13121629

**AMA Style**

Dabiri S, Noorpoor A, Arfaee M, Kumar P, Rauch W.
CFD Modeling of a Stirred Anaerobic Digestion Tank for Evaluating Energy Consumption through Mixing. *Water*. 2021; 13(12):1629.
https://doi.org/10.3390/w13121629

**Chicago/Turabian Style**

Dabiri, Soroush, Alireza Noorpoor, Maziar Arfaee, Prashant Kumar, and Wolfgang Rauch.
2021. "CFD Modeling of a Stirred Anaerobic Digestion Tank for Evaluating Energy Consumption through Mixing" *Water* 13, no. 12: 1629.
https://doi.org/10.3390/w13121629