A novel digital design methodology that combines computational fluid dynamics (CFD) modelling and Taguchi-Grey relational analysis method was presented for a single-strand tundish. The present study aimed at optimizing the flow control device in the tundish with an emphasis on maximizing the inclusion removal rate and minimizing the dead volume fraction. A CFD model was employed to calculate the fluid flow and the residence-time distribution of liquid steel in the tundish. The Lagrangian approach was applied to investigate the behavior of non-metallic inclusions in the system. The calculated residence-time distribution curves were used to analyze the dead volume fraction in the tundish. A Taguchi orthogonal array L9(3^4) was used to analyze the effects of design factors on both single and multiple responses. Moreover, for the purpose of meeting the multi-objective target functions, grey relational analysis and analysis of variance were used. The optimum positions of the weir and the dam were obtained based on the design targets. A special focus of this study was to demonstrate the capabilities of the Taguchi-Grey relational analysis method as a powerful means of increasing the effectiveness of CFD simulation.