Application of Wall Functions for Investigating Surface Roughness Effects on Spreading of an Impacting Droplet

The spreading dynamics of droplet impact on a solid surface is of great importance in applications such as printing, spray cooling, coating process and anti-icing. These phenomena have been studied in several investigations and aspects such as the effect of critical weber number on droplet break-up or the air bubble entrainment phenomenon as well as the influence of surface roughness. While experimental studies using surface roughness values ranging from $R_a = 0.003 \mu m$ to $25 \mu m$ were conducted, a few analytical approaches are available taking into account roughness effects in correlations. Contrary to this, considering roughness physically in simulations requires large calculation capability, time for geometry preparation as well as the reconstruction of varying topographical combinations is rather difficult and needs to be elaborated broadly. Therefore, the present study recommends a time-saving approach in OpenFOAM in which surface roughness is not represented physically in the domain, rather taken into account in a wall function term. The results of the study are in good agreement of $\pm10\%$ with the experimental data and mathematical models found in literature. Single drop impact simulations were carried out over a range of Weber number from 106 to 298 indicate that as \emph{We} number increases, the effect of the surface roughness on the spreading process diminishes.