Numerical investigation of three dimensional viscoelastic free surface flows: impacting drop problem

Abstract

This work presents a numerical investigation of three dimensional viscoelastic free surface flows. In particular, using two different numerical methodologies, we have simulated a typical free-surface benchmark flow problem: the impact of a viscoelastic fluid droplet with a rigid boundary. The numerical method was recently proposed by Figueiredo et al. [1] and has been implemented in a in-house viscoelastic flow solver. In this methodology, a finite difference scheme is adopted combining the Marker-And-Cell (MAC) method with a Front-Tracking strategy. In order to preserve mass conservation properties for transient viscoelastic fluid flows, we have modified the methodology in [1] to include an improvement on the MAC discretization of the velocity boundary conditions at free-surfaces. The code is verified by solving the drop impact problem for a Newtonian fluid. After this verification, we employ the Oldroyd-B model to assess the differences between the methodologies, and compare our results with the ones in the literature. Finally, a detailed study of the influence of the relevant rheological parameters of the non-linear viscoelastic models (Giesekus and XPP) is reported, regarding the deformation and spreading of the viscoelastic fluid drop after impacting on a rigid surface.