Critical review on CFD-based blast furnace mathematical models： challenges, developments and prospects

The blast furnace（BF） remains the dominant reactor for global hot metal production, yet its internal high-temperature, high-pressure, multiphase-coupled "black box" nature renders direct measurement extremely difficult. Computational fluid dynamics （CFD） full-scale blast furnace models have therefore become an indispensable tool for revealing in-furnace phenomena details and supporting operational decision-making. This paper systematically reviews the development history of CFD blast furnace mathematical models based on the transient/steady multi-fluid model framework, categorising their evolution into three generations. The first generation comprised steady-state models, which underwent continuous expansion from one-dimensional gas-solid systems to three-dimensional gas-solid-liquid-powder multiphase systems, incorporating dozens of chemical reactions and phase transformation processes. A key milestone of this generation was the introduction of a layered reacting structure across the entire furnace, assigning independent chemical reaction systems to ore layers and coke layers, respectively, which significantly improved the descriptive accuracy of cohesive zone morphology and gas flow distribution. The second generation was the transient model capable of simulating the dynamic response of the BF internal state following changes in operating parameters, such as sudden blast temperature drops, wet burden charging and hydrogen injection. This generation achieved simultaneous advancement in spatial dimensionality and physical fidelity. The third generation comprised intelligent models integrating machine learning, which used high-fidelity CFD simulation data as training sources to construct surrogate models capable of near-real-time prediction of full in-furnace state distributions, laying the foundation for the next version and real blast furnace digital twins. In practical applications, the selection of blast furnace models should be guided by specific industrial requirements. It should also be noted that the development of high-fidelity blast furnace models typically represents years of dedicated research efforts by academic institutions and is associated with a high barrier to reproduction, relying on long-term systematic accumulation of knowledge. As such, collaboration between industry and universities provides an effective pathway for the development and application of blast furnace mathematical models. This paper also identifies key challenges facing model development, including the balance between fidelity and computational efficiency, insufficient validation methods, model sustainability, and the construction of physics-constrained AI（artificial intelligence） integration frameworks, and provides an outlook on the development direction of intelligent blast furnace simulation platforms oriented towards industrial deployment.