Refinement of Modified Froude‐Number Scaling for Buoyancy‐Dominated Bottom Gas Stirring in Steelmaking

ABSTRACT

Bottom‐gas blowing is a key technology for green steelmaking because it enhances bath mixing, accelerates interfacial transport, improves temperature and composition homogenization, and reduces unnecessary gas consumption and over‐treatment. Cross‐medium scaling is therefore essential for translating observable water‐model behavior to opaque, high‐temperature molten baths. The modified Froude number, , remains useful when the momentum of the injected gas is dynamically important; however, its applicability becomes limited in buoyancy‐dominated bottom stirring, where plume growth, entrainment, viscosity, and surface tension also influence the flow. This study revises the similarity framework by combining bubble‐plume theory with the density‐corrected inertial group (G) correction for ladle systems. The resulting criterion is evaluated using large‐eddy simulation coupled with the volume‐of‐fluid method (LES‐VOF) simulations for molten steel, water, and glycerol–water analogs, as well as water‐model measurements under representative single‐nozzle conditions. The results show that the proposed scaling preserves plume width, centerline velocity, and bubble‐plume spreading more consistently than scaling under the investigated conditions. Although the framework is intended for single‐hole, buoyancy‐dominated bottom‐blown systems, it does not eliminate the need for additional validation in multi‐nozzle, slag‐containing, or reactive industrial ladles.