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In this paper, the instability of wave motion on the surface of liquid sheet emanating from a swirl injector exposed to inner and outer air streams, before the breakup is considered using the linear instability analysis by a perturbation method. The forces acting on a liquid gas interface in sprays, including surface tension, pressure, inertia force, centrifugal force and viscous force, lead to grow the disturbances originated from inside the injector on the outgoing liquid sheet. Interaction between these forces ultimately breaks up the jet into the ligaments. The linear instability analysis used in the present study is different from prior analysis. A cylindrical liquid sheet has been considered in previous studies but the present study implements the linear instability on a conical annular liquid sheet. Due to the complexity of derived governing equations a semi-analytical and numerical method was utilized in the solution procedure. The present model is capable to solve governing equations for the liquid jet with large range of spray angle. The predicted results compared with the prior studies results and experiments. The results of the current model in comparison with prior models have better accordance with experimental data. Also, the results show that the improved linear theory (the present model) predicts the breakup length better than linear theory.

Keywords: Spray, Linear Instability Analysis, Primary Breakup

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