Abstract The presence of space charge can cause a non-negligible effect in some electrospray applications, which, however, was ignored in previous numerical studies. In the present study, the formation of the cone-jet in the electrospray process is investigated with considering the space charge effects. The governing equations of fluid flow and electrostatics are coupled in the numerical method. The charge transport equation is implemented with no simplification and the volume of fraction (VOF) method is employed to track the liquid-gas interface. An improved model of considering the effect of charged droplet emitted from the tip of cone-jet on the external electric field is proposed. By considering the space charge effects, the improved model can achieve better accuracy in predicting the shape of the cone-jet by reducing the mean relative error from 12.5% to 4.2%. The flow field in the cone-jet is obtained and the vortices are found to play an important role in the cone-jet formation. In terms of the current produced by the cone-jet, the prediction error is reduced from 19 %-39% to 10 %-16% by considering the space charge. Further validation is conducted by comparing the simulated results with the prediction of the scaling laws. It was found that the prediction of the improved model fits better with the scaling laws based on both the analytical and experimental results. The new model can provide more reliable and detailed information for the simulation of other processes in the electrospray, i.e., the jet breakup and droplets motion.

中文翻译：

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空间电荷作用下电喷雾锥射流形成预测的改进模型

摘要 空间电荷的存在在一些电喷雾应用中会引起不可忽视的影响，然而，在以前的数值研究中却被忽略了。在本研究中，考虑到空间电荷效应，研究了电喷雾过程中锥形射流的形成。流体流动和静电的控制方程在数值方法中耦合。电荷传输方程的实现没有简化，并且采用体积分数 (VOF) 方法来跟踪液气界面。提出了一种考虑锥形射流尖端射出的带电液滴对外电场影响的改进模型。通过考虑空间电荷效应，改进后的模型通过将平均相对误差从 12.5% 降低到 4.2%，可以在预测锥形射流形状方面取得更好的精度。获得了锥形射流中的流场，发现涡流在锥形射流的形成中起重要作用。对于锥形射流产生的电流，考虑空间电荷，预测误差从19%-39%降低到10%-16%。通过将模拟结果与缩放定律的预测进行比较，进行进一步的验证。结果表明，基于分析和实验结果，改进模型的预测更符合标度定律。新模型可以为模拟电喷雾中的其他过程，即射流破碎和液滴运动提供更可靠和详细的信息。获得了锥形射流中的流场，发现涡流在锥形射流的形成中起重要作用。对于锥形射流产生的电流，考虑空间电荷，预测误差从19%-39%降低到10%-16%。通过将模拟结果与缩放定律的预测进行比较，进行进一步的验证。结果表明，基于分析和实验结果，改进模型的预测更符合标度定律。新模型可以为模拟电喷雾中的其他过程，即射流破碎和液滴运动提供更可靠和详细的信息。获得了锥形射流中的流场，发现涡流在锥形射流的形成中起重要作用。对于锥形射流产生的电流，考虑空间电荷，预测误差从19%-39%降低到10%-16%。通过将模拟结果与缩放定律的预测进行比较，进行进一步的验证。结果表明，基于分析和实验结果，改进模型的预测更符合标度定律。新模型可以为模拟电喷雾中的其他过程，即射流破碎和液滴运动提供更可靠和详细的信息。通过考虑空间电荷，预测误差从19%-39%降低到10%-16%。通过将模拟结果与缩放定律的预测进行比较，进行进一步的验证。结果表明，基于分析和实验结果，改进模型的预测更符合标度定律。新模型可以为模拟电喷雾中的其他过程，即射流破碎和液滴运动提供更可靠和详细的信息。通过考虑空间电荷，预测误差从19%-39%降低到10%-16%。通过将模拟结果与缩放定律的预测进行比较，进行进一步的验证。结果表明，基于分析和实验结果，改进模型的预测更符合标度定律。新模型可以为模拟电喷雾中的其他过程，即射流破碎和液滴运动提供更可靠和详细的信息。