A new energy-based model to predict spray droplet diameter in comparison with momentum-based models

To estimate mean droplet diameter (MDD) of a spray, three different numerical models were used in this paper. One of them is investigation of the surface instability of the liquid sheet producing from an injector.

First, the linear instability (LI) analysis introduced by Ibrahim (2006) is implemented. Second, the improved (ILI) analysis already introduced by the present authors is used. ILI analysis is different from the prior analysis, so that the instability of hollow-cone liquid sheet with different cone angles is investigated rather than a cylindrical liquid sheet. It means that besides the tangential and axial movements, radial movements of the liquid sheet and gas streams have been considered in the governing equations. Beside LI theory as a momentum-based approach, a new model as a theoretical energy-based (TEB) model based on the energy conservation law is proposed in this paper.

Based on the energy-based approach, atomization occurs because of kinetic energy loss. The resulting formulation reveals that the MDD is inversely proportional to the atomization efficiency and liquid Weber number.

The results of these three models are compared with the available experimental data. Prediction obtained by the proposed TEB model is in reasonable agreement with the result of experiment.

The results of these three models are compared with the available experimental data. Prediction of the proposed energy-based theoretical model is in very good agreement with experimental data.

Comparison between the results of new model, experimental data, other previous methods show that it can be used as a new simple and fast model to achieve good estimation of spray MDD.