Mathematical Modeling of Impinging Gas Jets on Liquid Surfaces

In top-blowing operations, the gas jet is a major source of momentum, so to model the momentum exchange properly with the liquid, the full-stress boundary conditions must be applied. A new mathematical method for better representation of the surface boundary condition was developed by combining the Cartesian cut cell method and volume of fluid method. The computational code was validated with the broken dam problem and reported critical phenomena in wave generation. The model was applied to impinging jets on liquid surfaces in two dimensions. The cavity depth was in good agreement with experimental measurements. The process of ligament and droplet formation was reproduced. The extent of momentum transfer to the liquid was investigated, and the trends with lance height and gas flow rate were similar to experimental evidence. The following important aspects of momentum transfer were identified: surface roughness as well as the development of local pressure gradients around wave crests. Kelvin–Helmholtz instability theory was used to interpret the results with respect to critical velocity for the onset of droplet formation. These principles were extended to conditions relevant to basic oxygen furnace (BOF) steelmaking. The critical velocities for droplets were calculated as functions of the physical properties for the gas–steel, gas–slag, slag–steel interfaces. The implications for BOF steelmaking were discussed. The mathematical model was applied to a simplified configuration of full-scale BOF steelmaking, and the local force balance was well described.