Insights into sloshing impact pressures through level set modeling of liquid droplet impacting a wall

This research arose from the need to understand the behavior of impact pressure caused by droplets formed during liquid sloshing in a tank. The two phase problem of a cylindrical liquid droplet of diameter D surrounded by a lighter fluid medium, impacting at some angle on a solid wall is studied. The incompressible two-dimensional continuity and Navier Stokes equations are solved by a two-step projection predictor-corrector algorithm, with a third-order Total Variation Diminishing (TVD) Runge-Kutta method for time stepping. The interface of the droplet is tracked by the zero contour of a level set function, which is allowed to evolve over time. Numerical simulation of impact pressure was found to agree well with the measured pressures, in particular at lower droplet velocities where compressibility effects can be ignored. A parametric study was conducted with a droplet of diameter 0.01 m traveling at four different impact angles between 45-90°. Velocities from 3.0-6.0 m/s, corresponding to Reynolds numbers from 2.9E05-4.8E05, and Weber numbers 1.25E04-5.0E05 were considered. The simulated impact pressure maximum plotted against the normal velocity of incidence shows a power law type behavior that is quite insensitive to the density ratio of the two fluids. The relationship between the velocity of the sloshing wave front and resultant pressure obtained from an experiment was found to be well predicted by the power law relationship for the liquid droplet impact.