Modeling of Droplet Dynamics in Secondary Breakup Process

A new droplet breakup model is presented for modeling temporal evolution of droplet in Bag regime. Despite of widely application of traditional methods such as Volume of Fluid (VoF) to multi-phase flow simulations, the implementation of these methods for resolving secondary breakup stage in spray simulations are very expensive due to huge number of droplets occupying the solution domain. In this regards, droplet breakup models merely considers the most fundamental physical mechanisms of breakup so that the computational costs reduce drastically. The purpose of current study is to model the fluid structure occurring in Bag breakup regime. This is achieved by introducing a two-degree-of-freedom (Two-DoF) system which is governed by a kinematic set of ordinary differential equations (ODEs). The dynamics formulation is based on virtual work principle. A reasonable profile is used for estimating pressure distribution on the droplet surface which enables the calculation of disrupting aerodynamic force. Finally, the governing kinematic equation is solved by using a fourth-order Runge-Kutta method. Results show a good agreement between numerical results and experiments. The time evolution of lateral and longitudinal deformations of droplet is well predicted by present model. Using a calibration factor improves the results further and the overall profile of the droplet matches that of observed in the experiments. The critical Weber number is also calculated by the model with an acceptable accuracy and the estimation of breakup time is improved in compared to other models. Overall, achievements of the present work indicate the appropriateness of the approach for the usage in CFD codes.

Keywords:

Droplet Deformation , Bag Breakup Regime , Shock tube experiments