A 1D analytical model for slag infiltration during continuous casting of steel is developed to investigate the slag behavior in the mold–strand gap. The superposition principle and Fourier expansion are applied to obtain the analytical solution for transient slag flow under arbitrary mold oscillation including non-sinusoidal oscillation mode. The validated model using literature data partially explains several controversies such as slope of slag film channel, mechanism of non-sinusoidal mold oscillation, and timing of slag infiltration. The model shows that a converging slag film into the casting direction is required to open the mold–strand gap if compression is applied in between. Also, model calculations imply that higher slag consumption is achievable from non-sinusoidal mold oscillation by means of the increase of film thickness through longer positive pressure with higher peak pressure. The model demonstrates a time difference between slag flow and pressure near the meniscus and the discrepancy in timing of infiltration between previous works is attributed to the mismatch. The model provides a concise but reliable tool to understand slag infiltration behavior and design mold oscillation settings.

中文翻译：

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非正弦结晶器振动下钢水连铸过程中熔渣渗入的一维解析模型

建立了钢连铸过程中炉渣渗入的一维分析模型，以研究铸型-钢坯间隙中炉渣的行为。运用叠加原理和傅立叶展开法，得到了包括非正弦振动模态在内的任意结晶器振动下的瞬态渣流的解析解。使用文献数据验证的模型部分解释了一些争议，例如渣膜通道的坡度，非正弦结晶器振动的机理以及熔渣渗透的时间。该模型表明，如果在两者之间施加压力，则必须在铸模方向上形成一层熔渣膜以打开铸模-铸坯间隙。也，模型计算表明，通过更长的正压和更高的峰值压力来增加膜厚，可以通过非正弦模具振动实现更高的炉渣消耗。该模型证明了弯液面附近熔渣流量与压力之间的时间差，并且先前工作之间的渗透时间差异是由于不匹配造成的。该模型提供了一个简洁而可靠的工具来了解炉渣的渗透行为并设计结晶器振动设置。