Figure 1

Relevant entities in the definition of the buoyancy force. Top left: Sketch of the 3d ladle with two eccentric nozzles; top right: The function \(r_{c}\); bottom: The functions \(\gamma _{i}(\cdot,z)\) (left) and \(\alpha _{i}(\cdot,x,y,z)\) (right) for a constant gas flow rate \(Q_{i}=17~{\mathrm{l}.\mathrm{min}^{-1}}\) (as in Table 1), where \(r_{xy}\) is the horizontal distance to the nozzle, i.e., \(r_{xy}^{2}=(x-x_{ni})^{2}+(y-y_{ni})^{2}\)