Dimensional analysis of the vertical heterogeneous buoyant plume

Starting from known features of homogeneous jets, the appropriate equations for the plume radius, the axial velocity and the volumetric flow capacity of the heterogeneous plume are developed by introducing a dimensionless product group. The factors and exponents connected with this group are adjusted by linear regression of data measured on water models. The own measurements show that the plume slowly performs inclinations and rotations. The limits of application for the derived equations are determined quantitatively. Here, a sufficiently low value of the gas volume fraction is decisive. The slip velocity between the bubbles and the plume is discussed. Finally, the theory is extended to the gas stirring of liquid steel. In this case, the high pressure decrease for the rising bubbles has to be taken into account.