Inclusion Capture Probability Prediction Model for Bubble Floatation in Turbulent Steel Flow
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hcr ¼ 2:33 108 ½1000rð1 cos hÞ0:16 ;
Inclusion Capture Probability Prediction Model for Bubble Floatation in Turbulent Steel Flow HAOJIAN DUAN, YING REN, and LIFENG ZHANG The turbulent flow around bubbles is simulated for the fixed turbulent kinetic energy. Inclusion motion through the flow field is studied by considering the stochastic effect of turbulence to calculate the capture probability of inclusions with different sizes to a fixed-size individual bubble according to the redefinition. Using the cubic spline interpolation, the capture probability is predicted as functions of the bubble size, inclusion size and turbulent kinetic energy. https://doi.org/10.1007/s11663-018-1462-x The Minerals, Metals & Materials Society and ASM International 2019
Removal of as many as inclusions possible from molten steel is a principal steelmaking objective since inclusions can lead to serious defects in the final product.[1] Gas injection is an effective approach to remove inclusions from the melt and widely used in secondary refining and continuous casting processes.[2] Based on the results from the field of mineral processing, Zhang and Taniguchi[3] extensively reviewed and studied the fundamentals of inclusion removal from liquid steel by bubble flotation. For successful attachment, the formation and the rupture of the liquid film play a central role. The film drainage time, tF, is the period required for drainage of the liquid film before the critical film thickness is reached and rupture occurs. Schulze[4] derived the film drainage time as tF ¼
3 a2 3 l d 64 Crh2cr p
2 a ¼ arccos41 1:02
dp qp u2R 12r
½1 !1=2 3 5
½2
HAOJIAN DUAN, YING REN, and LIFENG ZHANG are with the School of Metallurgical and Ecological Engineering, University of Science and Technology Beijing, Beijing 100083, China. Contact e-mails: [email protected]; [email protected] Manuscript submitted September 30, 2018. Article published online November 30, 2018. 16—VOLUME 50B, FEBRUARY 2019
½3
where tF is the film drainage time, (s); a is the angle for the transition of the spherically deformed part of the bubble surface to a nonspherically deformed state (rad); hcr is the critical thickness of liquid film for film rupture (m); l is the viscosity of liquid steel (PaÆs); r is the surface tension of liquid steel (N/m); h is the contact angle of the inclusions at the bubble–steel interface (deg); C is a constant and takes the value 4 for a free gas bubble; dp is the diameter of inclusion (m); qp is the density of inclusion (kg/m3); and uR is the relative velocity between the bubble and the inclusion (m/s). The process of inclusion removal by bubble flotation is conventionally characterized by the attachment probability. Inclusion capture by bubble wakes also plays a key role in inclusion removal. Hence, this is a narrow expression. The conventional theory for the classic attachment probability is defined as the fraction of inclusions that pass the rising bubble and attach to it, which is related to the conditions of laminar fluid flow[2]: Pcl ¼
NO dC ¼ ; N
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