A two-dimensional process of dyeing yarn coils was modelled in COMSOL Multiphysics to evaluate the dyeing characteristics according to a pilot-scale process. The proposed mathematical model was able to reproduce the experimental data and great importance was identified for the dyebath flow through the axial exit of the coil in relation to the radial outlet, about 2.8 times greater. To maintain the same flow, the permeability of the bobbin decreased tenfold between the radial and two-dimensional flow. Changes in the pressure gradient greatly influence the velocity field. The velocity and concentration fields found reinforce the preferential use of dyeing bobbins that do not have gaps between them, forcing the dyeing bath to follow the radial flow.

中文翻译：

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渗透性和压力对双向流动中腈纶纱筒子染料浓度分布的模拟影响

在 COMSOL Multiphysics 中对纱线线圈的二维染色过程进行建模，以根据中试规模的过程评估染色特性。所提出的数学模型能够重现实验数据，并且确定了通过线圈轴向出口相对于径向出口的染浴流的重要性，大约是径向出口的 2.8 倍。为了保持相同的流动，线轴的渗透率在径向和二维流动之间降低了十倍。压力梯度的变化极大地影响速度场。发现的速度和浓度场加强了优先使用它们之间没有间隙的染色筒管，迫使染色浴遵循径向流动。