Drop impact onto a liquid layer of finite thickness: Dynamics of the cavity evolution

Abstract

In the present work experimental, numerical, and theoretical investigations of a normal drop impact onto a liquid film of finite thickness are presented. The dynamics of drop impact on liquid surfaces, the shape of the cavity, the formation and propagation of a capillary wave in the crater, and the residual film thickness on the rigid wall are determined and analyzed. The shape of the crater within the film and the uprising liquid sheet formed upon the impact are observed using a high-speed video system. The effects of various influencing parameters such as drop impact velocity, liquid film thickness and physical properties of the liquids, including viscosity and surface tension, on the time evolution of the crater formation are investigated. Complementary to experiments the direct numerical simulations of the phenomena are performed using an advanced free-surface capturing model based on a two-fluid formulation of the classical volume-of-fluid (VOF) model in the framework of the finite volume numerical method. In this model an additional convective term is introduced into the transport equation for phase fraction, contributing decisively to a sharper interface resolution. Furthermore, an analytical model for the penetration depth of the crater is developed accounting for the liquid inertia, viscosity, gravity, and surface tension. The model agrees well with the experiments at the early times of penetration far from the wall if the impact velocity is high. Finally, a scaling analysis of the residual film thickness on the wall is conducted demonstrating a good agreement with the numerical predictions.

Dropwise condensation heat transfer process optimisation on superhydrophobic surfaces using a multi-disciplinary approach

“…In this model an additional convective term originating from modelling the velocity in terms of weighted average of the corresponding liquid and gas velocities is introduced into the transport equation for phase fraction, providing a sharper interface resolution. The model makes use of the two-fluid Eulerian model for two-phase flow, where phase fraction equations are solved separately for each individual phase (see [24]); hence the equations for each of the phase fractions can be expressed as where the subscripts l and g denote the liquid and gaseous phase, respectively. Assuming that the contributions of the liquid and gas velocities to the evolution of the free surface are proportional to the corresponding phase fraction, and defining the velocity of the effective fluid in a VOF model as a weighted average Equation 6 can be rearranged and used as an evolution equation for the phase fraction , where = is the vector of relative velocity, designated as the "compression velocity".…”

Lagrangian versus Eulerian integration errors

“…In order to emphasize the differences between the errors introduced in the spacetime integration for large time-steps using a Lagrangian or an Eulerian frame, the current case was also simulated with a large range of time-steps using PFEM-2 and comparing with results obtained by the widely known OpenFOAM code. The solver InterFOAM was chosen, which implements a Volume of Fluid (VoF) algorithm for multi-fluid flows [36] [37]. Another relevant feature to take into account when comparing both algorithms is that similar CPU times are required to solve a time-step.…”

A Numerical Investigation of Through-Tool Coolant Wetting Behaviour in Twist-Drilling

“…The presented VOF formulation has been evaluated against a range of multiphase flow problems, such as modulated jets [16], droplet impact and crater formation [17], film falling over turbulence wires [18] and inertia dominated and surface tension dominated flow regimes [19].…”