# Resolved Simulation for the Prediction of Classification in Decanter Centrifuges

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Numerical Setup

- A1
- Neglect of the gas phase;
- A2
- Same shape and density of all particles;
- A3
- Incompressibility of the particles and the fluid;
- A4
- No mass transfer between the components;
- A5
- Model the interactions between the disperse and the continuous phase by an additional transport equation for the solids volume fraction;
- A6
- Neglect of wall effects.

#### 2.2. Experimental Setup

^{3}m

^{−1}. The particle size distribution was measured with a laser diffraction spectrometer based on HELOS technology (Sympatec, Clausthal-Zellerfeld, Germany), which covers a measuring range from 20 nm to 20 µm. A LIQXI wet dosing unit directs the sample into a flow cell to dilute the suspensions to a suitable concentration. The laser diffraction sensor contains a blue light source and additional multi-element photodetectors for the detection of forward, wide-angle and backward scattered light signals. For each sample, at least five consecutive measurements were performed, whereby the measured light signal was corrected with the signal of a reference measurement without particles [54,55].

#### 2.3. Computational Geometries and Discretization

## 3. Results and Discussion

#### 3.1. Determination of the Material Functions

^{−4}and ${r}_{4}=-0.7$.

#### 3.2. Influence of the Number of Transported Particle Classes

^{−1}. It is recognizable that both the centrate and the sediment can be represented through the simulation. As observed in the simulation of the beaker centrifuge, the accuracy increases with a greater number of particle size classes. However, the most significant deviation is evident in the simulation with ten unevenly distributed particle size classes. An improved representation of centrate and sediment was expected due to the increased number of support points in that region. The simulation data solely fall within the size range of the experimental data but do not accurately reflect their trend. Similar to the beaker centrifuge, the distribution curve is much steeper. It is therefore not advisable to divide the particle size classes unevenly. Also notable is the significant deviation of the smallest support point for the centrate in the division into twenty particle size classes. For the smaller fractions, the chosen measurement method may not be optimal and a more precise resolution may be required.

#### 3.3. Mechanical Dewatering and Clarification

^{−1}. Shown in orange is the dependence of the solids volume fraction in the sediment and in blue is the solids volume fraction in the centrate on the rotational speed. The axes are scaled differently accordingly. Furthermore, triangular markers indicate the simulation results, while circles indicate the experimental results. As expected, the solids fraction in the sediment increases with the rising rotational speed. At the same time, the solids fraction in the centrate decreases. The reason for this is that with higher speeds, increasingly smaller particles are separated. In addition, a higher centrifugal force acts on the sediment, which is why it is compressed more. The simulation reproduces the experimental data well with the deviations being highest at 1000 rpm. In total, the simulation tends to underestimate the solids volume fractions in the sediment determined in the experiment. This may be related to additional shear compression in the apparatus [47,62] which was not taken into account in the material characterization. At lower speeds, the simulation overestimates solids volume fraction in the centrate. The simplifications made for the simulation may be responsible for the deviations in the centrate. For example, the gas phase was neglected and the overflow from the liquid weir was set at a constant level and also designed more generously. On the one hand, it was necessary to ensure that there were enough cells to map the outlet with sufficient accuracy. On the other hand, these cells should not be too small to avoid increasing the computing time.

#### 3.4. Simulation of the Classification Process

^{−1}and 5 rpm. As expected, the particle size distribution shifts towards smaller particles as the rotational speed increases. This means that more particles were separated. Overall, the simulation matches the experimental data. The deviations between simulation and experiment are consistent with the results regarding the solids volume fraction in centrate and sediment. There is a tendency for the particle size distribution to shift to the right towards larger particle sizes at lower rotational speeds and to the left towards smaller particle sizes at higher rotational speeds. It is also noticeable that with increasing rotational speed and the associated shift of the particle size distribution to the left, the lowest support point moves further upwards. For 1000 and 2000 rpm, it is still below 20%, for 4000 and 5000 rpm, just above 40%. For higher accuracy, it is recommended to simulate with more particle size classes for future simulations.

^{−1}, the lowest support point is just over 40%. Consequently, the simulation of the classification is limited to a certain extent by the number of particle size classes.

^{−1}. It is clearly evident that the suspension becomes clearer as the number of turns passed increases, as shown by the shift of the particle size distribution to the left. Notably, the diagram reveals that a substantial portion of particle separation occurs within the first three segments. The efficiency of particle separation decreases in the later segments, with the majority of separation processes taking place in the early segments. This is confirmed by the relative distance between the distributions. After each segment, fewer particles are separated progressively.

#### 3.5. Outlook: Geometry Optimization

^{−1}, constant differential speed of 5 rpm and an initial solids volume fraction of 2 $\mathrm{vol}\%$. It is apparent that with a higher rotational speed, the separation efficiency rises for all three geometries. Simultaneously, it is noticeable that the modified flights significantly enhance the separation performance. For example, approximately the same separation efficiency is achieved at 1000 rpm as with the conventional flight at 2000 rpm or a slightly better one at 2000 rpm than at 4000 rpm with the solid flight. Furthermore, the tapered flight seems to perform slightly worse at lower rotational speeds than the flight with windows only. However, as indicated by Figure 15, the re-suspension of already separated particles at the weir plate plays a crucial role, and enhanced clarification could be achieved by implementing an additional continuous axial discharge for the centrate.

## 4. Conclusions and Outlook

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Appendix A. Mesh Characteristics

Inlet | Outlet | Rotating Walls | Stationary Walls | |
---|---|---|---|---|

${\mathit{u}}_{\mathrm{mix}}$ | flowRateInletVelocity | zeroGradient | movingWallVelocity | noSlip |

p | fixedFluxPressure | fixedValue | fixedFluxPressure | fixedFluxPressure |

$\varphi $ | fixedvalue | zeroGradient | zeroGradient | zeroGradient |

${f}_{bk}\left(\varphi \right)$ | zeroGradient | zeroGradient | zeroGradient | zeroGradient |

${\sigma}_{e}^{\prime}\left(\varphi \right)$ | zeroGradient | zeroGradient | zeroGradient | zeroGradient |

**Figure A1.**Mesh independence study: (

**a**) the axial velocity component ${U}_{\mathrm{ax}}$ and (

**b**) the solids volume fraction $\varphi $ are plotted against the radial position r in the screw channel [36].

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**Figure 3.**Mesh of the decanter centrifuge generated with ANSYS DesignModeler. To obtain a structured mesh consisting of hexahedrons, the geometry was divided into 368 segments. As an example, two sections of the mesh are shown enlarged. The magnification factor is about six.

**Figure 4.**Discretization of the particle size distribution of limestone, by one (

**a**), three (

**b**), five (

**c**), ten (

**d**,

**e**) and twenty (

**f**) particle classes.

**Figure 5.**Influence of the solids volume fraction on the hindered settling velocity for different particle size classes of a limestone–water suspension.

**Figure 6.**Solids effective stress as a function of the solids volume fraction for the product limestone.

**Figure 7.**Influence of the number of particle size classes on the sediment structure in the beaker centrifuge: The solids volume fraction of the suspension was ${\varphi}_{0}=0.08$, the rotational speed was $n=2000$ min

^{−1}. The asterisk (*) indicates a non-homogeneously discretized distribution according to Figure 4e.

**Figure 8.**Particle size distribution in the individual sediment layers: The solids volume fraction of the suspension was ${\varphi}_{0}=0.08$, the rotational speed was $n=2000$ min

^{−1}. Ten particle size classes were used for the discretization.

**Figure 9.**Influence of the number n of particle size classes on the particle size distribution in the centrate and the sediment: the solids volume fraction of the feed suspension was ${\varphi}_{0}=0.02$, the volume flow rate was $\dot{V}=36$ Lh

^{−1}and the rotational speed was $n=3000$ min

^{−1}. The asterisk (*) indicates a non-homogeneously discretized distribution according to Figure 4e.

**Figure 10.**Required computation time for the simulation of the beaker centrifuge and the decanter centrifuge depending on the number of particle size classes. The asterisk (*) indicates a non-homogeneously discretized distribution according to Figure 4e.

**Figure 11.**Solids volume fraction of the centrate (blue) and the sediment (orange) at a volumetric flow rate of 36 Lh

^{−1}with varying rotational speed: Comparison of simulation and experiment.

**Figure 12.**Influence of the rotational speed n on the particle size distribution of the centrate: The solids volume fraction of the feed suspension was ${\varphi}_{0}=0.02$, the volume flow rate was $\dot{V}=36$ Lh

^{−1}and the rotational speed varies between 1000 rpm and 5000 rpm.

**Figure 13.**Influence of the rotational speed n on the particle size distribution of the centrate: The solids volume fraction of the feed suspension was ${\varphi}_{0}=0.02$, the rotational speed was $n=3000$ rpm and the volume flow rate varies between 24 Lh

^{−1}and 72 Lh

^{−1}.

**Figure 14.**Particle size distribution of the centrate in different segments in the decanter centrifuge: The solids volume fraction of the feed suspension was ${\varphi}_{0}=0.02$, the volume flow rate was $\dot{V}=36$ Lh

^{−1}and the rotational speed was $n=5000$ $\mathrm{rpm}$.

**Figure 15.**Solid distribution in the cylindrical section of the decanter centrifuge with various flight designs. The color scale indicates the solids volume fraction in the apparatus. The sediment ($\varphi >{\varphi}_{\mathrm{gel}}$) is shown in gray.

**Figure 16.**Separation efficiency for different flight designs of the screw: The solids volume fraction of the feed suspension was ${\varphi}_{0}=0.02$, the volume flow rate was $\dot{V}=36$ Lh

^{−1}.

Parameter | Symbol | Unit | Limestone |
---|---|---|---|

Particle size | ${x}_{50,3}$ | μm | 3 |

Density of limestone | ${\rho}_{\mathrm{p}}$ | kg m^{−3} | 2700 |

Density of water | ${\rho}_{\mathrm{l}}$ | kg m^{−3} | 1000 |

Gel point | ${\varphi}_{\mathrm{gel}}$ | - | $0.2$ |

Maximum concentration | ${\varphi}_{\mathrm{max}}$ | - | 1 |

Hindered settling parameter | ${r}_{2}$ | - | 15 |

Hindered settling parameter | ${r}_{3}$ | - | 1.3 × 10^{−4} |

Hindered settling parameter | ${r}_{4}$ | - | −0.7 |

Consolidation parameter | ${p}_{1}$ | Pa | 32 |

Consolidation parameter | ${p}_{2}$ | - | 9 |

Yield point | $\tau $ | Pa | 1 |

Consistency | k | m^{2} s^{−1} | 0.001 |

Rheological exponent | ${n}_{\mathrm{rheo}}$ | - | 1 |

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**MDPI and ACS Style**

Baust, H.K.; Nirschl, H.; Gleiß, M.
Resolved Simulation for the Prediction of Classification in Decanter Centrifuges. *ChemEngineering* **2024**, *8*, 48.
https://doi.org/10.3390/chemengineering8030048

**AMA Style**

Baust HK, Nirschl H, Gleiß M.
Resolved Simulation for the Prediction of Classification in Decanter Centrifuges. *ChemEngineering*. 2024; 8(3):48.
https://doi.org/10.3390/chemengineering8030048

**Chicago/Turabian Style**

Baust, Helene Katharina, Hermann Nirschl, and Marco Gleiß.
2024. "Resolved Simulation for the Prediction of Classification in Decanter Centrifuges" *ChemEngineering* 8, no. 3: 48.
https://doi.org/10.3390/chemengineering8030048