An equation for the floating velocity of cluster-shaped alumina inclusions which considers changes in average density was derived by quantifying the size and density of alumina clusters using fractal theory. The results obtained showed that the dependency of the floating velocity on the cluster diameter is smaller than in the conventional equations, which assume that clusters have a uniform average density. In particular, the floating velocity of clusters 100 μm and over is considerably smaller than the conventional floating velocity.
A model of the coalescence of cluster-shaped inclusions was also constructed, and the behavior of alumina clusters in molten steel in the tundish of an actual continuous casting machine was analyzed considering floating characteristics and agglomeration. The calculated results showed good agreement with the results measured in the actual machine, demonstrating that it is possible to simulate the coalescence and floating separation of cluster inclusions in molten steel with this model.