# Numerical Simulation and Application of an Oxygen-Enriched Side-Blown Smelting Furnace for the Treatment of Electroplating Sludge

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Model Establishment and Calculation

#### 2.1. Geometry Model with Simplification

#### 2.2. Grid Division and Independence Test

#### 2.3. Mathematic Model and Calculation Method

#### 2.3.1. Basic Governing Equations

- (1)
- Continuity Equation

^{3}, ${v}_{\mathrm{m}}$ is the velocity of the mixture phase, m/s, and $t$ is the time, s.

- (2)
- Volume Fraction Equation

^{3}; t is the time, s; $\nabla $ represents the operator symbol whose expression is $\nabla =\left(\frac{\partial}{\partial x}+\frac{\partial}{\partial y}+\frac{\partial}{\partial y}\right)$; ${\overrightarrow{v}}_{q}$ is the velocity of phase q, m/s; ${\dot{m}}_{pq}$ represents the mass transfer from phase p to phase q; ${\dot{m}}_{qp}$ is the mass transfer from phase q to phase p; and ${S}_{{\alpha}_{q}}$ is the constant or user-defined mass source for each phase.

- (3)
- Momentum Equation

^{3}; $\overrightarrow{v}$ is the velocity of the fluid, m/s; $\mu $ represents the dynamic viscosity, Pa·s; $\overrightarrow{g}$ is the gravitational acceleration, m/s

^{2}; and $\overrightarrow{F}$ is the volume force acting on the control volume, N.

#### 2.3.2. Turbulence Model

^{−1}·s

^{−3}); ${G}_{b}$ represents the generation of turbulence kinetic energy due to buoyancy, kg·(m

^{−1}·s

^{−3}); ${Y}_{M}$ is the contribution of the fluctuating dilatation in compressible turbulence to the overall dissipation rate; ${C}_{2}$ and ${C}_{1\epsilon}$ are constants; ${\sigma}_{k}$ and ${\sigma}_{\epsilon}$ represent the turbulent Prandtl numbers for k and ε, respectively; ${S}_{k}$ and ${S}_{\epsilon}$ are user-defined source terms; ${\mu}_{t}$ is the turbulent viscosity, Pa·s; ${\mu}_{t}=\rho {C}_{\mu}\frac{{k}^{2}}{\epsilon}$; and $\mu $ represents dynamic viscosity, Pa·s.

#### 2.3.3. Boundary Conditions and Property Parameters of Material

- (1)
- Inlet conditions

- (2)
- Outlet conditions

- (3)
- Wall boundary conditions

- (4)
- Material

#### 2.3.4. Solver Settings

#### 2.4. Establishment of the Water Model

^{−2}; $L$ is the characteristic length, mm; and $\frac{{\rho}_{g}}{{\rho}_{l}}$ is the gas–liquid density ratio. In the oxygen-enriched side-blown smelting process:

#### 2.5. Numerical Simulation

#### 2.5.1. Basic Working Conditions

#### 2.5.2. Single-Factor Numerical Experiment

#### 2.5.3. Multifactor Comprehensive Optimization

- (1)
- Definition I: Indicator layer matrix M

_{i}can be defined as k

_{ij}(l = 4, m = 3). The larger the three evaluation indicators of the orthogonal experimental results were, the better; this led to K

_{ij}= k

_{ij}and established the matrix.

- (2)
- Definition II: Factor layer matrix $T$

- (3)
- Definition III: Level layer matrix $S$

_{i}in the orthogonal experiment was set as s

_{i}, where ${S}_{i}={s}_{i}/{\displaystyle \sum _{i=1}^{l}{s}_{i}}$, and established the matrix.

- (4)
- Definition IV: Weight matrix $\omega $

## 3. Results and Discussion

#### 3.1. Grid Independence Test

#### 3.2. Model Verification

#### 3.3. Flow Field and Temperature Distribution under Basic Working Conditions

#### 3.3.1. Variation in Gas Volume Fraction Distribution with Time

#### 3.3.2. Gas Volume Fraction Distribution

#### 3.3.3. Velocity Distribution

#### 3.3.4. Temperature Distribution

#### 3.4. Analysis and Optimization of Key Parameters

#### 3.4.1. Lance Diameter

#### 3.4.2. Lance Inclination

^{2}/s

^{2}. This variation was only about 13–17% compared with the range under other influential factors (0.036 m

^{2}/s

^{2}under the diameter of the oxygen lance and 0.029 m

^{2}/s

^{2}under the depth of the molten pool). Therefore, it can be concluded that the lance inclination of about 15° was best.

#### 3.4.3. Bath Depth

#### 3.4.4. Lance Spacing

#### 3.5. Matrix Analysis of the Orthogonal Experimental Results

_{1}B

_{2}C

_{3}D

_{2}, and the corresponding parameters were a lancing diameter of 25 mm, lance inclination of 15°, lance spacing of 1050 mm, and bath depth of 1500 mm.

#### 3.6. Industrial Application Verification

_{2}S, NiS, and elemental copper, which proves that the product is matte and is similar to the composition of industrial matte products. It can be seen from Table 10 that the main elements of slag are Fe, SiO

_{2}, and CaO. Compared with industrial copper slag, the content of CaO in slag melted by electroplating sludge is higher, while the content of Fe is lower. The XRD pattern shows that the main material is wollastonite and olivine, and contains a small amount of silica, which can be used for cement raw materials and building materials.

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 4.**Connection diagram of the water model experimental device (

**a**): 1—High speed camera. 2—Computer. 3—Water model of side-blown furnace. 4—LED light source. 5—Rotor flow meter. 6—Air pump. The schematic of the water model of the side-blown furnace (

**b**).

**Figure 7.**Comparison of bubble shapes in numerical simulation and water model experiment (

**a**), (

**b**) initial blowing stage; and (

**c**,

**d**) continuous blowing stage.

**Figure 8.**Schematic diagram of the sections of the furnace: lance cross-section (

**a**), bath-free surface (

**b**), and lance longitudinal sections (

**c**,

**d**).

**Figure 10.**Gas volume fraction distribution of lance cross-section (

**a**), bath-free surface (

**b**), and lance longitudinal sections (

**c**,

**d**) in the furnace.

**Figure 11.**Velocity distribution of lance cross-section (

**a**), bath-free surface (

**b**), and lance longitudinal sections (

**c**,

**d**) in the furnace.

**Figure 13.**Relationship between average velocity (

**a**), turbulent kinetic energy (

**b**), bath gas rate (

**c**), and lance diameter.

**Figure 14.**Relationship between average velocity (

**a**), turbulent kinetic energy (

**b**), bath gas rate (

**c**), and lance inclination.

**Figure 15.**Relationship between average velocity (

**a**), turbulent kinetic energy (

**b**), bath gas rate (

**c**), and bath depth.

Zone | Scheme Elements | Scheme Type | Interval Size/Count | Quantity of Elements |
---|---|---|---|---|

Gaseous area | hexahedral | Map | Size: 20 | 117,600 |

Melt area | Tet/Hybrid | TGird | Size: 6 | 570,629 |

Lance area (Face mesh) | Quadrilateral | Pave | Count: 30 | \ |

Lance area | Hex/Wedge | Cooper | Size: 4 | 6068 × 10 |

Fluid | Density/ (kg·m ^{−3}) | Temperature/ K | Viscosity/ (kg·m ^{−1}·s^{−1}) | Specific Heat Capacity/ (J·kg ^{−1}·K^{−1}) | Thermal Conductivity/ (W·m ^{−1}·K^{−1}) |
---|---|---|---|---|---|

Copper Matte | 4600 | 1573.15 | 0.0022 | 607 | 0.04381 |

Oxygen-enriched Air | 1.235 | 298.15 | 1.817 × 10^{−5} | 967.854 | 0.02444 |

Factors | Level 1 | Level 2 | Level 3 |
---|---|---|---|

A Lance Diameter/mm | 25 | 30 | 35 |

B Lance Inclination/° | 12 | 15 | 18 |

C Lance Spacing/mm | 850 | 950 | 1050 |

D Bath Depth/mm | 1450 | 1500 | 1550 |

Experiment Number | Level of Lance Diameter | Level of Lance Inclination | Level of Lance Spacing | Level of Bath Depth |
---|---|---|---|---|

1 | 1 | 1 | 1 | 1 |

2 | 1 | 2 | 2 | 2 |

3 | 1 | 3 | 3 | 3 |

4 | 2 | 1 | 2 | 3 |

5 | 2 | 2 | 3 | 1 |

6 | 2 | 3 | 1 | 2 |

7 | 3 | 1 | 3 | 2 |

8 | 3 | 2 | 1 | 3 |

9 | 3 | 3 | 2 | 1 |

Element Number | 322,445 | 748,909 | 1,044,726 |
---|---|---|---|

Average Velocity (m/s) | 0.37 | 0.319 | 0.32 |

Result | Water Model Experimental | Numerical Simulation | Error/% |
---|---|---|---|

d_{b}/d_{n} ^{1)} | 6.93 | 7.1 | 2.39 |

^{1)}$d\mathrm{b}$: bubble diameter; $dn$: lance diameter.

Experiment Number | Lance Diameter /mm | Lance Inclination /° | Lance Spacing /mm | Bath Depth /mm | Average Velocity /ms ^{−1} | Turbulent Kinetic Energy /m ^{2} s^{2} | Bath Gas Rate /% |
---|---|---|---|---|---|---|---|

1 | 1 | 1 | 1 | 1 | 0.248 | 0.0275 | 6.87 |

2 | 1 | 2 | 2 | 2 | 0.272 | 0.0333 | 7.91 |

3 | 1 | 3 | 3 | 3 | 0.280 | 0.0316 | 8.02 |

4 | 2 | 1 | 2 | 3 | 0.249 | 0.0218 | 7.61 |

5 | 2 | 2 | 3 | 1 | 0.233 | 0.0251 | 6.68 |

6 | 2 | 3 | 1 | 2 | 0.270 | 0.0258 | 7.64 |

7 | 3 | 1 | 3 | 2 | 0.314 | 0.0162 | 7.48 |

8 | 3 | 2 | 1 | 3 | 0.291 | 0.02 | 8.21 |

9 | 3 | 3 | 2 | 1 | 0.241 | 0.0178 | 7.23 |

K1 | 0.2667 | 0.2703 | 0.2697 | 0.2407 | Intuitive analysis of average velocity | ||

K2 | 0.2507 | 0.2653 | 0.254 | 0.2853 | |||

K3 | 0.282 | 0.2637 | 0.2757 | 0.2733 | |||

R | 0.0313 | 0.0066 | 0.0217 | 0.0446 | |||

K1 | 0.0308 | 0.0218 | 0.0244 | 0.0235 | Intuitive analysis of turbulent kinetic energy | ||

K2 | 0.0242 | 0.0261 | 0.0243 | 0.0251 | |||

K3 | 0.018 | 0.0251 | 0.0243 | 0.0245 | |||

R | 0.0128 | 0.0043 | 0.0001 | 0.0016 | |||

K1 | 7.6 | 7.32 | 7.5733 | 6.9267 | Intuitive analysis of bath gas rate | ||

K2 | 7.31 | 7.6 | 7.5833 | 7.6767 | |||

K3 | 7.64 | 7.63 | 7.3933 | 7.9467 | |||

R | 0.33 | 0.31 | 0.19 | 1.02 |

Elements | Fe | Ca | Cu | Al | Si | Sn | Mg | Ni | Mn | C | S |
---|---|---|---|---|---|---|---|---|---|---|---|

Wt% | 10.34 | 10.95 | 6.64~7.50 | 2.51 | 1.61 | 0.86 | 0.91 | 0.50 | 0.37 | 7.58 | 5.89 |

**Table 9.**Element analysis results of matte products [29].

Smelting Method | Chemical Composition/wt% | |||||
---|---|---|---|---|---|---|

Cu | Fe | S | Ni | Zn | Pb | |

ES | 46.56 | 21.21 | 21.98 | 3.11 | 0.07 | 0.06 |

Closed blast furnace (Oxygen-enriched air) | 41.57 | 28.66 | 23.79 | - | - | - |

Otokunp | 52.46 | 19.81 | 22.37 | 0.23 | ||

Vanukov | 41–55 | 25–14 | 22–24 | 4.5–5.2 | - | - |

Ausmelt | 44.50 | 23.60 | 23.80 | - | 3.20 | - |

Mitsubishi | 65.70 | 9.20 | 21.90 | - | - | - |

**Table 10.**Analysis results of copper slag composition [29].

Smelting Method | Chemical Composition/wt% | |||||||
---|---|---|---|---|---|---|---|---|

Cu | Fe | Fe_{3}O_{4} | SiO_{2} | S | Al_{2}O_{3} | CaO | MgO | |

ES | 0.27 | 25.86 | 36.5 | 0.3 | 5.9 | 19.5 | 0.95 | |

Closed blast furnace (Oxygen-enriched air) | 0.42 | 29.00 | - | 38.0 | - | 7.5 | 11.0 | 0.74 |

Vanukov | 0.45 | 35.00 | 3.15 | 35.0 | 0.7 | 3.8 | 8.0 | 1.40 |

Otokunp | 0.78 | 44.06 | - | 29.7 | 1.4 | 7.8 | 0.6 | - |

Mitsubishi | 0.60 | 38.20 | - | 32.2 | 0.6 | 2.9 | 5.9 | - |

Ausmelt | 0.65 | 34.00 | 7.50 | 31.0 | 2.8 | 7.5 | 5.0 | - |

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## Share and Cite

**MDPI and ACS Style**

Yang, B.; Liu, W.; Jiao, F.; Zhang, L.; Qin, W.; Jiang, S.
Numerical Simulation and Application of an Oxygen-Enriched Side-Blown Smelting Furnace for the Treatment of Electroplating Sludge. *Sustainability* **2023**, *15*, 10721.
https://doi.org/10.3390/su151310721

**AMA Style**

Yang B, Liu W, Jiao F, Zhang L, Qin W, Jiang S.
Numerical Simulation and Application of an Oxygen-Enriched Side-Blown Smelting Furnace for the Treatment of Electroplating Sludge. *Sustainability*. 2023; 15(13):10721.
https://doi.org/10.3390/su151310721

**Chicago/Turabian Style**

Yang, Biwei, Wei Liu, Fen Jiao, Lin Zhang, Wenqing Qin, and Shanqin Jiang.
2023. "Numerical Simulation and Application of an Oxygen-Enriched Side-Blown Smelting Furnace for the Treatment of Electroplating Sludge" *Sustainability* 15, no. 13: 10721.
https://doi.org/10.3390/su151310721