Towards Real-Time Digital Twins in Steelmaking: The Role of Reduced Order Methods in Continuous Casting Tundish Process

Continuous casting is the predominant method used in steel production, accounting for 96% of the world’s steel production. Within this process, the continuous casting tundish plays a critical role as a metallurgical reactor in the continuous casting process, with its flow characteristics serving as a key parameter in the production of high-quality steel. During a typical production cycle, the tundish undergoes one steady-state operation and three transient operations, occurring during the initial filling, ladle changeover, and final emptying phase. This work particularly focuses on the phenomena associated with steady-state operation and the ladle changeover transient operations. The steady-state operation is the most prevalent stage during the production cycle, while the ladle changeover transient operation typically lasts no more than 10-15 minutes. In steady-state operation, the key flow characteristics are typically evaluated using residence time distribution (RTD) curves. This study investigates fluid flow in a single-strand tundish through mathematical modelling, validated against water-model experiment results. Full-order steady simulations were carried out under both isothermal and non-isothermal conditions to assess the influence of thermal buoyancy on flow behavior. The results indicate that buoyancy effects under non-isothermal conditions have a negligible impact on the overall velocity field. The resulting steady-state flow fields were then used to perform transient tracer transport simulations to derive RTD curves and volume partitioning. Additionally, a sensitivity analysis is conducted to examine the effect of inlet velocity on RTD characteristics. In the ladle changeover transient operation, the key quantity of interest is steel grade intermixing, particularly the new steel grade transition at the outlet of the tundish. Accurate prediction of grade intermixing during ladle changeover operations is critical for maintaining steel quality and minimizing material losses in the continuous casting process. Among various factors influencing grade intermixing, operating parameters play a significant role, in addition to tundish geometry and flow control devices. In this study, three-dimensional, transient, multi-phase turbulent flow simulations are conducted to investigate the ladle changeover operation. During this process, the molten steel level in the tundish typically varies over time, significantly affecting the grade intermixing phenomena. The influence of ladle change time on intermixing time has been presented. To address the high computational cost associated with the full-order industrial-scale simulations of both steady-state and transient ladle changeover operations of the tundish, reduced order methods are exploited. These methods enable efficient evaluation of key flow characteristics, such as RTD curves and steel grade intermixing time. For the steady-state operation RTD analysis, both projection-based model order reduction and data-driven reduced order model (ROM) strategies are explored. For parameter-time dependent RTD analysis, a projection-based ROM and data-driven model approach are employed to capture the flow characteristics within the tundish system. For the transient ladle changeover operation, a data-driven ROM approach is developed using reservoir computing (RC), specifically echo state networks (ESNs), in combination with proper orthogonal decomposition (POD). This POD–RC–ROM framework enables rapid prediction of new steel grade evolution and intermixing times, demonstrating strong potential for real-time process monitoring and optimization in continuous casting operations. Advection-dominated problems are typically noticed in nature, engineering systems, and industrial processes. However, traditional linear model reduction methods, such as proper orthogonal decomposition and reduced basis methods, are ill-suited for these problems, due to slow Kolmogorov n-width decay, leading to inefficient and inaccurate ROMs. To address this, two advanced non-linear model reduction strategies are proposed in this work. The first approach proposes the complete neural network shift-proper orthogonal decomposition based reduced order model algorithm, consisting of offline-online stages. It utilizes a neural-networks shift augmented transformation technique for automatic shift detection. This method learn a parameter dependent mapping between the original solution manifold and a transformed manifold, where linear compression techniques are more effective. The second method employs cross-correlation based snapshot registration to align transported features to a reference frame, accelerating the Kolmogorov n-width decay and enabling the construction of efficient ROMs using linear methods. Both methods offer complete offline-online stages for the development of non-intrusive or data-driven ROM. The effectiveness of these approaches is demonstrated on several benchmark problems, including the 1D linear advection equation, the 2D isentropic convective vortex, and a 2D two-phase flow scenario inspired by the flow physics within a tundish.