Study on the Pouring Characteristics of Ladles with Non-Cylindrical Inner Surfaces Based on the Gauss Divergence Theorem

Intermittent tilting pouring is widely utilized in metal casting due to its operational simplicity and cost-effectiveness. However, this method faces challenges such as difficult manual tuning and inconsistency in achieving constant flow rates. Targeting pouring equipment at a high-purity metal smelting company, this study proposes a closed-surface flux calculation method based on the Gauss divergence theorem to determine molten metal volume at any given instant. A mathematical model for pouring processes involving ladles with non-cylindrical inner surfaces is established. Based on this model, pouring characteristics are analyzed. Through piecewise fitting, angular velocity functions for constant flow rate pouring are derived, which provides theoretical guidance for practical industrial operations.