# A Mathematical Model Combined with Radar Data for Bell-Less Charging of a Blast Furnace

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## Abstract

**:**

## 1. Introduction

## 2. Mathematical Model and Radar Data Treatment

#### 2.1. Mathematical Model Structure

#### 2.1.1. Burden Flow Trajectory Model

_{0}) can be described by the hydraulic formula [22]:

#### 2.1.2. Burden Profile Model

#### 2.1.3. Burden Distribution Model

#### 2.1.4. Burden Evaluation Model

#### 2.2. Radar Detection Measurement

#### 2.2.1. Radar Data Collection

#### 2.2.2. Processing of Radar Data

#### 2.2.3. Burden Distribution Calculation

#### 2.3. Parameters of Blast Furnace and Assumptions of Calculation

## 3. Application of the Combined Model and Results

#### 3.1. Mathematical Model Test

#### 3.2. Combination of the Mathematical Model and Radar Data

## 4. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 4.**The trajectory of the material in the cavity, where ${h}_{0}$ is the distance from the chute suspension point to the zero value stock of the line (m), ${h}_{1}$ is the distance from the chute suspension point to the end of the chute (m), ${h}_{2}$ is the vertical distance of the material after leaving the chute tip (m), and $H$ is distance between the material and zero value of the stock line (m).

**Figure 5.**Schematic diagram of a new surface formation on an original one, where $\mathsf{\delta}$ is the repose angle of the burden. (

**a**) the location of the inner foot B is the intersection of the lower trajectory with the previous burden profile; (

**b**) the material keeps the repose angle slipping on the inner surface of the profile.

**Figure 8.**Procedure of the combination of the mathematical model and radar data in a software implementation.

**Figure 15.**Burden distribution by a multi-ring charging program based on Table 1, Table 2, Table 3 and Table 4: (

**a**) 1st ring of ore; (

**b**) a full burden distribution of an ore and a coke layer with multi-ring; (

**c**) 2 coke and 2 ore layers. Blue line: initial material surface. Blue dash-dotted line: wall. Green line: ore layer. Red line: coke layer.

**Figure 16.**(

**a**–

**h**) are the comparison of burden distributions corresponding to the charging matrix of (

**a**–

**h**) in Table 5.

**Figure 17.**Comparison of the burden distribution with different ore batches: (

**a**) Ore batch of 63 t; (

**b**) Ore batch of 55 t.

**Figure 19.**Burden profile: (

**a**) Burden profile from radar data; (

**b**) Burden profile from the mathematical model combined with radar data.

**Figure 20.**Visualization of our software by the combination of the mathematical model and radar data: (

**a**) Software login interface; (

**b**) Parameter setting interface; (

**c**) Burden distribution display and radar data monitor; (

**d**) User management interface.

Property | Value |
---|---|

Throat diameter (mm) | 8300 |

Throat height (mm) | 2600 |

Shaft angle (°) | 84.15 |

${D}_{c}$^{1} (mm) | 4010 |

${D}_{b}$^{2} (mm) | 1030 |

${D}_{z}$^{3} (mm) | 4601 |

^{1}Distance from throttle to chute suspension point.

^{2}Distance from the chute suspension point to the chute bottom plate.

^{3}Distance from the chute suspension point to the zero line.

Property | Value |
---|---|

The length of the chute (mm) | 3890 |

Chute speed ($\mathrm{r}\xb7{\mathrm{s}}^{-1}$) | 0.133 |

Coefficient of coke friction | 0.758 |

Coefficient of ore friction | 0.638 |

Velocity attenuation coefficient of coke | 0.70 |

Velocity attenuation coefficient of ore | 0.71 |

Property | Ore | Coke |
---|---|---|

Bulk density ($\mathrm{kg}/{\mathrm{m}}^{3}$) | 1800 | 550 |

Repose angle (°) | 31.5 | 32.5 |

Chute Angle (°) | 46 | 44 | 41.5 | 39 | 36.5 | 15 |
---|---|---|---|---|---|---|

Coke charging ring number | 2 | 2 | 2 | 2 | 2 | |

Ore charging ring number | 3 | 3 | 2 | 2 |

Figure No. | Inclination Angle of the Chute (°) | 41 | 39 | 37 | 34 | 31 | 27 | 20 | 12 |
---|---|---|---|---|---|---|---|---|---|

a | Ore | 2 | 3 | 3 | 2 | 1 | |||

Coke | 3 | 3 | 3 | 2 | 2 | 5 | |||

b | Ore | 2 | 3 | 3 | 2 | 1 | |||

Coke | 3 | 3 | 3 | 2 | 2 | 1 | 4 | ||

c | Ore | 2 | 3 | 3 | 2 | 1 | |||

Coke | 3 | 3 | 3 | 2 | 2 | 2 | 3 | ||

d | Ore | 2 | 3 | 3 | 2 | ||||

Coke | 3 | 3 | 3 | 2 | 2 | 3 | |||

e | Ore | 2 | 3 | 3 | 2 | 1 | |||

Coke | 3 | 3 | 3 | 2 | 2 | 3 | 2 | ||

f | Ore | 2 | 3 | 3 | 2 | 1 | |||

Coke | 3 | 3 | 3 | 2 | 2 | 2 | 2 | ||

g | Ore | 2 | 3 | 3 | 2 | 1 | |||

Coke | 3 | 3 | 3 | 2 | 2 | 2 | |||

Inclination angle of the Chute (°) | 40 | 38 | 36 | 33 | 30 | 27 | |||

h | Ore | 2 | 3 | 3 | 2 | 1 | |||

Coke | 3 | 3 | 3 | 2 | 2 | 2 |

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**MDPI and ACS Style**

Li, M.; Wei, H.; Ge, Y.; Xiao, G.; Yu, Y.
A Mathematical Model Combined with Radar Data for Bell-Less Charging of a Blast Furnace. *Processes* **2020**, *8*, 239.
https://doi.org/10.3390/pr8020239

**AMA Style**

Li M, Wei H, Ge Y, Xiao G, Yu Y.
A Mathematical Model Combined with Radar Data for Bell-Less Charging of a Blast Furnace. *Processes*. 2020; 8(2):239.
https://doi.org/10.3390/pr8020239

**Chicago/Turabian Style**

Li, Meng, Han Wei, Yao Ge, Guocai Xiao, and Yaowei Yu.
2020. "A Mathematical Model Combined with Radar Data for Bell-Less Charging of a Blast Furnace" *Processes* 8, no. 2: 239.
https://doi.org/10.3390/pr8020239