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Numerical Simulation of Droplet Splashing Behavior in Steelmaking Converter Based on VOF-to-DPM Hybrid Model and AMR Technique

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Abstract

Droplet splashing behavior caused by the top blowing supersonic jets impacting the liquid metal surface significantly affects the decarburization efficiency and refractory erosion during the basic oxygen furnace (BOF) steelmaking process. However, simulating the mass and size of splashing droplets is challenging because the droplet size differs by multiple orders of magnitude from the molten bath. Herein, a hybrid model (VOF-to-DPM) coupling the volume of fluid model (VOF) and discrete phase model (DPM) was combined with the adaptive mesh refinement (AMR) technique to successfully achieve high-resolution and quantitative capture of splashing droplets. The simulation results are in good agreement with the droplet splashing rate calculated by the theoretical formula based on the Blowing number (NB) within the allowable error range. The generation mechanisms of splashing droplets caused by single-hole and multiple-hole jets impacting the liquid surface were clarified. Furthermore, the effects of oxygen lance height and top blowing flow rate on the total droplet mass, mass and percentage of droplets sprayed on the furnace wall, and the droplet size were also investigated. It was revealed that with the decrease of the oxygen lance height, the total droplet mass increases and then decreases, and the droplet size increases. As the top blowing flow rate increases, the total mass and size of droplets both tend to increase. The proportion of droplets sprayed on the furnace wall increases sequentially when the impact cavities are in the penetrating mode, splashing mode, and quasi-dimpling mode. Moreover, the relationship between the cavity morphology and the droplet splashing was quantitatively characterized. As the modified cavity shape index (Icm) increases, the droplet splashing mass increases then decreases and finally increases. The change in cavity mode is the main factor affecting the droplet splashing behavior.

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Abbreviations

BOF:

Basic oxygen furnace

VOF:

Volume of fluid

DPM:

Discrete phase model

VOF-to-DPM:

Volume of fluid-to-discrete phase model

AMR:

Adaptive mesh refinement

RRS:

Rosin-Rammler sperling

CFD:

Computational fluid dynamics

RANS:

Reynolds averaged Navier-stokes

CSF:

Continuum surface tension

SST:

Shear stress transport

PISO:

Pressure implicit with splitting of operators

PRESTO!:

PREssure STaggering Option

CICSAM:

Compressive interface capturing scheme for arbitrary meshes

PUMA:

Polyhedral unstructured mesh adaption

HNA:

Hanging node adaption

MRL:

Maximum refinement level

FFT:

Fast Fourier transform

ρ g :

Density of gas phase (kg·m-3)

ρ l :

Density of liquid phase (kg·m-3)

μ g :

Dynamic viscosity of gas phase (Pa·s)

μ l :

Dynamic viscosity of liquid phase (Pa·s)

\(\overrightarrow{u}\)  :

Velocity vector (m·s-1)

\({\overline{\overline{\tau }}}\)  :

Viscous stress term (–)

g:

Gravitational acceleration (m·s-2)

f σ :

Surface tension (N·m-3)

P :

Static pressure (MPa)

σ :

Surface tension coefficient (N·m-1)

K :

Curvature (m-1)

\(\overrightarrow{\text{n}}\)  :

Surface normal vector (–)

\(\widehat{\text{n}}\) :

Unit vector normal to the interface (–)

m p :

Particle mass (kg)

τ r :

Relaxation time (s)

d p :

Particle diameter (m)

Re :

Relative Reynolds number (–)

C d :

Drag coefficient between particle and air (–)

a 1, a 2, a 3 :

Parameters varying with Reynolds number [43] (–)

u p :

Velocity of the discrete phase droplet (m·s-1)

V p :

Volume of continuous phase droplet (m3)

k :

Turbulent kinetic energy (m2·s-2)

ω :

Turbulent frequency (s-1)

σ k :

Prandtl numbers for turbulent kinetic energy (–)

σ ω :

Prandtl numbers for turbulent energy dissipation rate (–)

μ :

Dynamic viscosity of the fluid (Pa·s)

Ω:

Vorticity tensor (–)

y :

Distance to the wall (m)

σ k ,1, σ ω ,1, σ k ,2, σ ω ,2 :

Empirical constants, [45] and their respective values are1.176, 2.0, 1.0 and 1.168

F 1 and F 2 :

Mixing functions (–)

r i :

Vector pointing from the gravity center of the lump to every face center (–)

n i :

Face normal vector (–)

U g :

Critical velocity of gas (m·s-1)

R B :

Droplet splashing rate (kg·s-1)

F G :

Top gas flow rate (Nm·s-3)

N B :

Blowing number (–)

I cm :

Modified cavity shape index (–)

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Acknowledgments

This work is financial support by the National Natural Science Foundation of China (51974023) and Jiangxi Provincial Department of Science and Technology (20171ACE50020).

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The authors declare that they have no conflict of interest.

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Authors and Affiliations

  1. State Key Laboratory of Advanced Metallurgy, University of Science and Technology Beijing, Beijing, 100083, P.R. China

    Jiankun Sun, Jiangshan Zhang, Rui Jiang & Qing Liu

  2. Xinyu Iron and Steel Co., Ltd, Xinyu, 338001, Jiangxi, P.R. China

    Xiaoming Feng

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  1. Jiankun Sun
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Sun, J., Zhang, J., Jiang, R. et al. Numerical Simulation of Droplet Splashing Behavior in Steelmaking Converter Based on VOF-to-DPM Hybrid Model and AMR Technique. Metall Mater Trans B 55, 1098–1116 (2024). https://doi.org/10.1007/s11663-024-03024-2

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