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Nowadays, coherent and conventional supersonic jets are widely used in electric arc furnace (EAF) steelmaking processes. Generally, these jets are installed in the EAF oven wall with a tilt angle of 35–45°. However, limited studies have been conducted on the impact characteristics of these inclined supersonic jets. This study developed an optimized theoretical model to calculate the penetration depth of inclined coherent and conventional supersonic jets by combining theoretical modeling and numerical simulations. The computational fluid dynamics results are validated against water model experiments. A variable k is newly defined to reflect the velocity variation, which is related to the jet exit at the jet free distance. The results of the optimized theoretical model show that the lance height and lance angle influence the penetration depth of the inclined supersonic jet. At the same lance angle, the penetration depth decreases with the increase in the lance height. Similarly, it decreases with the decrease in lance angle at the same lance height. In addition, the penetration depth of an inclined coherent supersonic jet is larger than that of an inclined conventional supersonic jet under the same conditions. An optimized theoretical model can accurately predict the penetration depths of the inclined coherent and conventional supersonic jets.

Influence of lance height and angle on the penetration depth of inclined coherent and conventional supersonic jets in electric arc furnace steelmaking