Abstract A 3-D numerical model was established for predicting the flow field in a square electromagnetic cold crucible (EMCC) used for melting and directionally solidifying TiAl alloys. Four dimensionless parameters that characterise the melt flow in the EMCC were derived, those being the Hartman (Ha), magnetic Reynolds (Rω), coils-melt position (h) and the ratio of the melt height to length (H/L) numbers. Parametric simulations and experiments were carried out to understand the effects of processing parameters such as the intensity and frequency of the current, the relative coils-melt position and the melt shape on the flow field. The meridional flow normally consists of two vortices in the half meridian plane, the lower vortex decreases with increasing Ha, Rω and h ( h b > h m ), as well as decreasing H/L. Higher Ha, H/L and lower h induce intensive fluid flow in the melt due to the stronger EM coupling, which could promote the uniformity of solute in the melt. The turbulence kinetic energy is significantly influenced by the length scale of the turbulent flow and the flow velocity in the melt, it increases with increasing Ha, h and H/L, while reduces and tends to be stable at higher Rω. Relatively higher flow velocity and turbulence kinetic energy can be obtained when Rω is close to 10. The weakened flow in the vicinity of solid/liquid interface under lower Ha and Rω, as well as higher h and H/L is beneficial for continuous growth of columnar crystals during the directional solidification process.

中文翻译：

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控制电磁冷坩埚中流体流动的无量纲参数

摘要 建立了用于预测用于熔化和定向凝固 TiAl 合金的方形电磁冷坩埚 (EMCC) 中流场的 3-D 数值模型。推导出了表征 EMCC 中熔体流动的四个无量纲参数，这些参数是哈特曼 (Ha)、磁雷诺数 (Rω)、线圈-熔体位置 (h) 和熔体高度与长度之比 (H/L) 数. 进行参数模拟和实验以了解诸如电流强度和频率、相对线圈-熔体位置和熔体形状等工艺参数对流场的影响。经向流通常由半子午面的两个涡流组成，下层涡流随着 Ha、Rω 和 h 的增加而减小（ hb > hm ），以及 H/L 的减小。高哈，由于更强的电磁耦合，H/L 和较低的 h 在熔体中引起强烈的流体流动，这可以促进熔体中溶质的均匀性。湍流动能受湍流长度尺度和熔体中流速的显着影响，它随着Ha、h和H/L的增加而增加，而在较高的Rω下减小并趋于稳定。当 Rω 接近 10 时，可以获得相对较高的流速和湍流动能。较低的 Ha 和 Rω 下固/液界面附近的流动减弱，以及较高的 h 和 H/L 有利于连续生长定向凝固过程中的柱状晶体。湍流动能受湍流长度尺度和熔体中流速的显着影响，它随着Ha、h和H/L的增加而增加，而在较高的Rω下减小并趋于稳定。当 Rω 接近 10 时，可以获得相对较高的流速和湍流动能。较低的 Ha 和 Rω 下固/液界面附近的流动减弱，以及较高的 h 和 H/L 有利于连续生长定向凝固过程中的柱状晶体。湍流动能受湍流长度尺度和熔体中流速的显着影响，它随着Ha、h和H/L的增加而增加，而在较高的Rω下减小并趋于稳定。当 Rω 接近 10 时，可以获得相对较高的流速和湍流动能。较低的 Ha 和 Rω 下固/液界面附近的流动减弱，以及较高的 h 和 H/L 有利于连续生长定向凝固过程中的柱状晶体。