Abstract: A mathematical model for the gas-liquid flow field in the ladle with argon blowing and electromagnetic stirring was developed based on the Euler model and population balance model(PBM). The results show that the upward stirring only forms a large circulation flow field in the ladle， while the downward stirring forms a large and a small circulation flow fields. The size of the bubble in the center of gas-liquid region is the largest and is gradually reduced when the bubble is changed from the center to the boundary of the gas-liquid two-phase region. With increasing electromagnetic stirring current， the deflection degree in vertical direction in gas-liquid two-phase region is greater and the distribution of large-sized bubble area in the center of the gas-liquid two-phase region becomes wider. The area of large-sized bubbles in the central region from the downward stirring is smaller than that from the upward stirring. The spatial distribution of large-sized bubbles has less effect on the deflection and bends to the center line of the ladle.

Key words: electromagnetic stirring, ladle, bubble, breakage and coalescence, population balance model