# Agitation of Viscoplastic Fluid in a Rotating Vessel Using Close Clearance Agitators

## Abstract

**:**

## 1. Introduction

## 2. Numerical Modeling and Computational Settings

#### 2.1. Mechanical Agitation System

#### 2.2. Governing Equations

#### 2.3. Fluid Comportment

- Reynolds number:$$Re=\frac{\rho N{d}^{2}}{{\eta}_{\infty}}$$
- Bingham number:$$Bi=\frac{{\tau}_{0}}{{\eta}_{\infty}N}$$
- Nusselt number:$$Nu=\frac{{h}_{t}{D}_{v}}{\lambda}$$
- Power consumption:$$Np=\frac{P}{\rho {N}^{3}{d}^{5}}$$

#### 2.4. Solver Settings

^{−6}in order to satisfy the convergence criterion.

- On the impeller ${v}_{r}={v}_{t}=0$;
- On the vessel ${v}_{r}={v}_{t}=-2\pi NR$.

- On the impeller $\frac{\partial T}{\partial n}=0$;
- On the vessel $T=1$.

## 3. Results and Discussion

#### 3.1. Grid Independency and Numerical Validation

#### 3.2. Effect of Inertia

#### 3.3. Effect of Rheology

#### 3.4. Thermal Performance

#### 3.5. Power Consumption

## 4. Conclusions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**Geometry and presentation of the simulated systems: (

**a**) anchor impeller; (

**b**) gate impeller; and (

**c**) two-bladed impeller.

**Figure 5.**Stream function comparison for different Reynolds numbers: (

**a**) anchor impeller; (

**b**) gate impeller; (

**c**) two-bladed impeller.

**Figure 6.**Tangential velocity profiles on the impeller plane for the three impellers: (

**a**) Re = 13.8; (

**b**) Re = 416.

**Figure 7.**Tangential velocity profiles on the median plane for the three impellers: (

**a**) Re = 13.8; (

**b**) Re = 416.

**Figure 8.**Velocity contour distribution for different Bingham numbers: (

**a**) anchor impeller; (

**b**) gate impeller; and (

**c**) two-bladed impeller.

**Figure 9.**Velocity vector field and velocity contour distribution for different yield stress ${\tau}_{0}$: (

**a**) anchor impeller; (

**b**) gate impeller; and (

**c**) two-bladed impeller.

**Figure 10.**Temperature field comparison for different Reynolds numbers: (

**a**) anchor impeller; (

**b**) gate impeller; and (

**c**) two-bladed impeller.

**Figure 14.**Power consumption variation as a function of yield stress ${\tau}_{0}$ for the three impellers.

Impeller Type | Fluid Studied | Contribution | Refs. |
---|---|---|---|

Anchor-helical impellers | Shear-thinning fluid | Highlighted the pivotal role of impeller height in overall mixing system performance. | [7] |

Anchor impeller + Scaba 6SRGT | Shear-thinning fluid | Combined an anchor impeller with a Scaba 6SRGT turbine, achieving notable improvements in cavern size, especially near the impeller axis. | [8] |

Circular anchor impeller | Viscoplastic fluid | Conducted a numerical exploration of a circular-shape anchor impeller design for mixing yield stress fluids, presenting advantages such as improved flow field patterns and reduced energy consumption costs. | [9] |

Anchor impeller | Viscoplastic fluid | Determined optimal values for stirrer clearance and width-to-vessel diameter ratios. Found that the four-bladed anchor impeller outperformed the two-bladed variant in terms of mixing efficiency. | [10] |

Modified anchor impeller configuration | Shear-thinning fluid | Employed a modified impeller configuration and studied the impact of geometric design, anchor curvature, and shear zone on energy consumption. | [16,17] |

Double helical ribbon, anchor, gate, Maxblend impellers | Shear-thinning fluid | Investigated the flow energy efficiency. Maxblend impeller demonstrated superior mixing quality and lower energy consumption in cylindrical tanks. | [18] |

Anchor impellers with different blade shapes | Viscoplastic fluid | Compared different anchor blade shapes. The octagonal blade shape provided the broadest well-stirred region. | [19] |

Anchor agitators | Viscoplastic fluid | Explored rheological parameters effects on flow and power consumption. | [20] |

Anchor and paddle impellers | Mixing characteristic using tracer particles | Investigated geometric parameters’ impact on the anchor and plate impellers on fluid mixing characteristics, with a focus on achieving uniform fluid spreading. | [21] |

Anchor impeller with different horizontal blades | Viscoplastic fluid | Investigated different geometric designs and inclination angles of anchor blades. Found that the anchor impeller with a 60° inclination exhibited the most efficient acceleration of flow. | [22] |

Coaxial mixers: anchor with A200 impeller, ARI impeller and Rushton turbine | Shear-thinning fluid | Highlighted the significance of the interaction between the central impeller type and speed in determining coaxial power consumption. | [23] |

Coaxial mixers: CBY or Pfaudler impeller combined with anchor or helical ribbon | Shear-thinning fluid | Showed that the Pfaudler helical ribbon configuration stood out as the optimal choice, yielding the shortest mixing time with same power consumption. | [24] |

Scaba-anchor coaxial mixer | Shear-thinning fluid | Revealed that mixing efficiency was higher in the co-rotating mode compared to the counter-rotating mode. | [25,26] |

Coaxial mixers: anchor with Cowles turbine, four-pitched blade turbine or three-blade propeller impellers | Viscoelastic fluid | Showed that the four-pitched blade turbine combined with an anchor impeller achieved the shortest mixing time with less power consumption. | [27] |

D_{v} | d | d_{a}/D_{v} | e/D_{v} | L/D_{v} | W/D_{v} | c/D_{v} |
---|---|---|---|---|---|---|

300 mm | 288 mm | 0.023 | 0.027 | 0.067 | 0.02 | 0.167 |

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**MDPI and ACS Style**

Benmoussa, A.
Agitation of Viscoplastic Fluid in a Rotating Vessel Using Close Clearance Agitators. *Eng* **2023**, *4*, 2525-2541.
https://doi.org/10.3390/eng4040144

**AMA Style**

Benmoussa A.
Agitation of Viscoplastic Fluid in a Rotating Vessel Using Close Clearance Agitators. *Eng*. 2023; 4(4):2525-2541.
https://doi.org/10.3390/eng4040144

**Chicago/Turabian Style**

Benmoussa, Amine.
2023. "Agitation of Viscoplastic Fluid in a Rotating Vessel Using Close Clearance Agitators" *Eng* 4, no. 4: 2525-2541.
https://doi.org/10.3390/eng4040144