论文标题

对湿墙的降落影响:一种基于停滞点流的牙冠扩展建模的分析解决方案

Drop impact on wetted walls: An analytical solution for modelling the crown spreading based on stagnation-point flow

论文作者

Lamanna, G., Geppert, A., Bernard, R., Hörner, I., Weigand, B.

论文摘要

提出了一种分析溶液来预测冠状的传播,这是由单滴对湿壁的影响产生的。这种方法使从惯性驱动到冠状传播的粘性控制状态的平稳过渡。该建模策略基于停滞点的流量,因为它与Lamella中的流体动力流相似,并提供了两个主要优势。首先,它可以简单地估算壁膜变薄速率,这是由于冲动从撞击液滴到壁膜的脉冲转移而引起的。其次,由于解决方案的自相似性,它可以直接估计沿墙壁散布的胶卷时动量损失。通过将此估计纳入现有的无关模型中,可以在整个皇冠高程阶段找到与实验的极好一致性。通常,分析表明,由于冠的大部分繁殖,尤其是对于薄壁薄膜,由于粘性效应引起的动量损失不能被忽略。所提出的方法为预测冠底底断裂(CBB)的建立铺平了道路。在这种情况下,由于孔的自发创建,冠状薄片直接在其底部瓦解,从而在破裂之前在Lamella中形成了类似网络的结构。我们的理论分析表明,冠状兰米拉的这种过早破裂与局部不稳定性效应有关,这是由于惯性力和表面张力之间的不平衡引起的。

An analytical solution is proposed to predict the crown propagation, generated by a single droplet impact on wetted walls. This approach enables a smooth transition from the inertia-driven to the viscous-controlled regime of crown propagation. The modelling strategy is based on the stagnation-point flow, because it resembles closely the hydrodynamic flow in the lamella and offers two main advantages. First, it allows a simple estimation of the wall-film thinning rate, caused by the impulse transfer from the impacting droplet to the wall film. Second, thanks to the self-similarity of the solution, it enables a straightforward estimation of momentum losses during film spreading along the wall. By incorporating this estimation into existing inviscid models, an excellent agreement with experiments is found during the entire crown elevation phase. In general, the analysis shows that momentum losses due to viscous effects cannot be neglected during a significant portion of crown propagation, particularly for thin wall films. The proposed methodology paves the way for predicting the inception of crown bottom breakup (CBB). In this case, the crown lamella disintegrates directly at its base due to the spontaneous creation of holes that create a web-like structure in the lamella prior to its break-up. Our theoretical analysis shows that this premature break-up of the crown lamella is associated to local instability effects, caused by the unbalance between inertial forces and surface tension.

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