Steady-state and transient solutions to drop evaporation in a finite domain: Alternative benchmarks to the d2 law

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.