Abstract The d2 law, commonly used to assess the accuracy of computational solvers, corresponds to evaporation under steady-state conditions and in an infinite gaseous domain. In the present work, we propose new alternative benchmarks that relax those constraints. The benchmarks are developed for a spherical as well as a circular drop. First, steady-state analytical relations are derived that are applicable to a finite domain. A radially-symmetric transient model is then proposed that can provide transient benchmark solutions in finite domains. Adaptive mesh-refinement and body-fitted mesh are used for numerical solution and to ensure highly accurate transient results. The proposed steady-state and transient benchmarks are examined in several evaporation problems, and the evolution of drop diameter, temperature and vapor mass fraction fields are analyzed. In one such problem, we report a secondary transient phenomenon that appears towards the end of drop lifetime. The benchmarks proposed in this work are straightforward to be implemented for systematic validation of computational solvers.

中文翻译：

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在有限域中降低蒸发的稳态和瞬态解决方案：d 2 定律的替代基准

摘要 通常用于评估计算求解器精度的 d2 定律对应于稳态条件下和无限气态域中的蒸发。在目前的工作中，我们提出了新的替代基准来放宽这些限制。基准是针对球形和圆形水滴开发的。首先，导出适用于有限域的稳态解析关系。然后提出了一个径向对称瞬态模型，该模型可以在有限域中提供瞬态基准解决方案。自适应网格细化和贴体网格用于数值求解并确保高度准确的瞬态结果。在几个蒸发问题中检查了提议的稳态和瞬态基准，以及液滴直径的演变，分析温度和蒸汽质量分数场。在一个这样的问题中，我们报告了在跌落寿命结束时出现的二次瞬态现象。这项工作中提出的基准很容易实现，用于计算求解器的系统验证。