A droplet deformation and breakup model based on virtual work principle

A new method of modeling the deformation and secondary breakup of a droplet is presented. The general formulation is based on the virtual work principle and potential flow assumption. To reach the final model, some approximations are made in the aerodynamic calculations including moderate Reynolds number of gas, Reg ∼ 1000, and high density ratio of liquid to gas phase, ρl/ρg ≫ 1. The dynamics of a drop is considered using two degrees of freedom. Two coupled ordinary differential equations are derived which describe time evolution of drop within both vibrational and bag regimes. The model is capable of keeping track of droplet deformation and distortion up to the onset of the bag rupture. The critical Weber number has been predicted with an error of around 20% as compared to the experimental data. The model performance is enhanced after a minor tuning, which result in the critical Weber number of 12.5. The predicted distortion quantities in lateral and longitudinal directions, as well as the drop profiles, are validated against experiments for bag and vibrational regimes. A good agreement is found between the computed results and experiments. Overall, achievements of the present work indicate a promising potential of the current approach for modeling droplet dynamics.