![]() ![]() 20) As a result, a constant inertial force was derived, which indicates that the inertial force on particles is independent of the inter-particle distance. used a 2nd order polynomial to fit the discrete inter-particle distance points. The inertial force on particles is calculated by the second derivative of the fitting function with respect to time, and then multiply the result with particles’ effective mass. 14, 19) To tackle this problem, a curve-fitting approach was proposed to represent the relationship between the inter-particle distance and time by a function. 6, 10, 14, 19) However, this method is very sensitive to the accuracy of the measured inter-particle distance, and therefore the inter-particle distance should be measured very accurately to avoid an unreasonable force oscillation. 7, 17, 18) In the metallurgical field, the lateral capillary force is usually assumed to be balanced by the inertial force calculated from three successive inter-particle distances with a known interval time and the effective particle mass. 6, 8) The capillary force can be theoretically calculated either from the interfacial force integration along the three-phase contact line and the pressure over particle surface or from the derivative of the free energy change with respect to the interparticle distance. The long-range lateral attractive force between inclusion particles is believed to be a kind of capillary force, which arises from the interface deformation due to the presence of particles. 6) Thereafter, the interaction of more complex types of inclusions was studied using a similar methodology, e.g., inclusions in the CaO–Al 2O 3–SiO 2, 6, 14) CaO–Al 2O 3–MgO–SiO 2 11, 15) and CaO–Al 2O 3–MnO–SiO 2 systems. 6, 8, 9, 10, 11, 12, 13) The pioneering experiment was done by Yin and co-workers, who studied the collision, agglomeration and clustering of alumina inclusion particles at the liquid steel and argon gas interface. For this purpose, many in-situ real-time observations of inclusion clustering on steel melt surface were performed with the help of high-temperature confocal scanning laser microscopy (CSLM). 6, 7) Thus, a better understanding of the clustering behavior at the liquid steel and inert gas interface is essential for steel cleanliness control. ![]() 5) During the inert gas injection, the interface of liquid steel and inert gas is an important site for inclusion clustering, where the deformation of the interface is usually detected inducing a strong lateral attractive force between the inclusions. However, it is more detrimental if these clusters remain in the solidified steel. 2, 3, 4) Clusters formed by the agglomeration of small inclusions are more readily floated to the melt surface or steel/slag interface. Inert gas injection is one of the most effective ways to remove the inclusions by enhancing bubble adherence and agitating turbulence flow to improve inclusion collision and flotation. 1) Complete removal of these inclusion particles is time-consuming and difficult in practice. The NMI in a steel melt are generated either during the deoxidation process or during reoxidation with the environment (atmosphere, slag and refractory). Steel cleanliness improvement by reducing non-metallic inclusions (NMI) is an important aspect of high-quality steel production. Among these functions, the 4th order polynomial and the 2nd order sine are the most robust functions in predicting the inertial force on particles, even when the measured distance is less accurate. Moreover, the curve fitting function is also considered in this study including the use of polynomial, exponential, sum of sines, rational, Gaussian functions and Fourier series. However, both the identical and non-identical force schemes tend to give an unreasonably oscillating force when the measured inter-particle distance is less accurate. Considering the nature of the attractive force, a new iteration scheme is proposed where the inertial force is assumed to be non-identical from point to point. In most of the studies, the inertial force is calculated from three successive inter-particle distances with a certain time interval, in which the inertial force is assumed to be identical at the first two distances. ![]() ![]() To predict the clustering of inclusions at the liquid steel and inert gas interface, it is essential to calculate the pairwise attractive (inertial) force on the inclusions correctly. ![]()
0 Comments
Leave a Reply. |