Grid dependence of evaporation rates in Euler–Lagrange simulations of dilute sprays

Abstract

The present study addresses the grid dependence of evaporation rates in the context of Euler-Lagrange simulations and presents error estimates as a function of characteristic parameters. The common approach of using local cell values as ambient conditions for the evaporation model and returning heat and mass to the gas phase via source terms, which is known as the particle-source-in-cell (PSI-cell) model, is not grid independent and leads to large deviations in the evaporation rates if the cell size is of the order of the droplet diameter. This problem has become increasingly important in recent years as increased computing power now allow direct numerical simulations of the carrier gas and large-eddy simulations with much smaller cell sizes to be used, making the point-source approximation increasingly inadequate. It is therefore necessary to estimate the error that is introduced by the PSI-cell model to be able to perform simulations with a given (and a priori known) error level. Focusing on a single droplet in an infinite environment, expressions are derived for the deviation of the evaporation rate and time compared to a reference solution for both quiescent and convective environments and including the effects of heat transfer. It is found that the error of the steady-state evaporation rate is a function of the ratio of cell size to droplet diameter and the cell Péclet number. The error of the evaporation time additionally depends on the initial ratio of liquid to gaseous mass in the computational cell and on the reference mass transfer number, whose influence can be combined in a modified mass ratio. The presented expressions are simple to use and valid across a wide range of gas and droplet properties that are typical for spray combustion applications and provide guidelines for the correct choice of the cell size in Euler-Lagrange simulations of dilute sprays.