The pressure and flow rate of an argon line embedded within a stopper rod serve as useful industrial indicators and control factors for mitigating air aspiration into the Submerged Entry Nozzle (SEN) during the continuous casting of steel. This manuscript investigates several challenges associated with interpreting monitored argon line pressures and gas flow rates, including variations in gas pressure during delivery, actual volumes of gas entering the nozzle, argon leakage, and air aspiration. To address these issues, a new one-dimensional (1D) analytical model of compressible argon flow in the stopper rod was developed, incorporating gas dynamics and heat transfer. This concise 1D model was validated using data from a continuous casting simulator (CCS) employing a low-melting-point Bi-Sn alloy (melting point 137 °C). Pilot trials were conducted to replicate various industrial casting scenarios, generating datasets for model validation and demonstration of real-time operation. The 1D model predictions were compared with those from a CFD-based compressible flow model under CCS operating conditions. Following validation, parametric studies were conducted to explore realistic industrial scenarios (e.g., gas flow rate < 5 SLPM, nozzle diameter < 5 mm), including extreme conditions such as air aspiration and choking: a critical nozzle diameter (1.223 mm) corresponds to choked flow, limiting the maximum achievable gas flow rate to 5 SLPM. Additionally, the real-time prediction capabilities of the model were demonstrated using measured argon line pressures and flow rates from CCS trials. The proposed 1D model thus provides a practical tool for accurately interpreting SEN flow conditions from monitored argon pressures and effectively estimating argon bubble injection by clarifying actual gas pressures and flow rates at the stopper injection point.

Electric smelting furnace (ESF) is a key technology in hydrogen-based steelmaking for green steel production owing to its capability to utilize lower-grade iron ores with high slag volumes, highlighting its growing importance as high-grade ore concentrates become scarce. However, the internal characteristics of ESF, particularly brush arc behavior and its interaction with the molten bath, remain insufficiently investigated due to the emerging nature of the process. To address this gap, a mathematical model integrating multiphase fluid flow, heat transfer, and magnetohydrodynamics was developed to simulate brush arc behavior in the vicinity of the electrode. By explicitly tracking bath surface deformation induced by arc jet impingement, the model predicts the transient evolution of electrical characteristics, including arc resistance and power, during arc–bath interactions. The validated model was applied to investigate arc instability under different operating modes (brush and open arcs) and bath types (flat, slag, and iron baths), demonstrating that both factors significantly influence arc characteristics. Based on the predicted arc current profile and corresponding Stability Factor of Current (SFC), the brush arc mode exhibited an average of 10.13% greater instability than the open arc mode, while different bath types produced variations of up to 8.82% through distinct instability mechanisms. The results further revealed that arc resistance is strongly coupled with arc instability through dynamic bath surface evolution. The unstable arc continuously deforms the cavity, which subsequently modifies the arc length, gas recirculation, and current path, establishing different arc–bath feedback mechanisms governing both arc resistance and instability.