On the analytical modelling of the initial ice growth in a supercooled liquid droplet
On the analytical modelling of the initial ice growth in a supercooled liquid droplet
复制标题
DOI：
10.1016/j.ijheatmasstransfer.2018.06.089
复制
发表时间：
2018-12-01
影响因子：
5.2
通讯作者：
Weigand, B.
中科院分区：
文献类型：
--
作者：
Schulte, K.;Weigand, B.
大气中常见的亚稳态、过冷液滴形成的冰会显着影响大气云的外观和特征，例如降水。其数值研究可以深入了解潜在的物理机制，并支持在微观尺度上描述这些过程的模型的推论；描述宏观物理系统需要这些模型。然而，即使是微观尺度的过程也跨越了大约四个数量级。因此，推导了基于相似解的半解析子尺度模型，以缩小描述过冷液滴中最初球形冰生长的不同尺度之间的差距，这可以简化为径向对称但高度非线性的Stefan型问题。所有相关的物理效应，例如与经典方法相比，考虑了熔化温度的降低、由于凝固时密度降低和高度过冷而导致的水相膨胀。明确给出的冻结时间以及温度场的最大相对误差在过冷度为 35 K 时小于 10%，并且随着环境温度的升高而迅速减小。 (C) 2018 Elsevier Ltd. 保留所有权利。
Ice formation in metastable, super-cooled droplets, which are frequently found in the atmosphere, influences the appearance and characteristics of atmospheric clouds significantly, for example regarding precipitation. Its numerical investigation can provide deep insight into the underlying physical mechanisms and supports the deduction of models that describe these processes on the microscale; those models are required for a description of the macrophysical system. However, even the processes on the microscale span about four orders of magnitude. A semi-analytical sub-scale model based on similarity solutions is thus deduced in order to narrow the gap between the different scales describing the initially spherical ice growth in a super-cooled droplet, which can be reduced to a radially symmetric, but highly non-linear Stefan-type problem. All relevant physical effects, e.g. the reduction of the melting temperature, the expansion of the water phase due to the decrease of density upon solidification and high degrees of supercooling, are taken into account in contrast to classical approaches. The maximum relative error in terms of the freezing time, which is given explicitly as well as the temperature fields, is less than 10% at a degree of supercooling of 35 K and decreases rapidly as the ambient temperature increases. (C) 2018 Elsevier Ltd. All rights reserved.