A Theoretical Scaling Equation for Designing Physical Modeling of Gas–Liquid Flow in Metallurgical Ladles. Issue 1 (19th July 2016) - Yu, Shan; Zou, Zong‐Shu; Shao, Lei; Louhenkilpi, Seppo
Abstract : The role of gas stirring in ladle metallurgy has been well appreciated and a great volume of pertaining studies have been carried out, mostly resorting to numerical modeling and/or physical modeling. As for physical modeling of gas–liquid flow in metallurgical ladles, a (conventional) scaling equation, i.e., Q ′ = λ L 2.5 Q, has been commonly adopted for determining experimental gas flow rate with respect to the one of the real ladle. Noticing that no physical properties are involved in the conventional scaling equation, two physical modeling systems with different liquids are collected in the literature in order to assess its applicability. It is shown that the conventional equation is still somewhat questionable. A theoretical scaling equation embodying liquid density and surface tension, i.e., Q ′ = ( λ σ / λ ρ ) 0.25 λ L 2 Q, is therefore deduced by analyzing the governing equation of plume rise velocity, which is also derived from fundamental laws of conservation. The advantage of the theoretical scaling equation is finally demonstrated by comparing the calculated order of prototype gas flow rate with the one based on measured gas fractions in the two systems. Abstract : In the present work, a theoretical scaling equation embodying liquid density and surface tension is deduced by analyzing the governing equation of plume rise velocity for physical modeling of gas–liquid flow in metallurgical ladles. The advantage of the scaling equation is demonstrated by comparing the calculated order of prototype gas flow rate with the one based on measured gas fractions.