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In jet atomization, breakup length is the length of the continuous jet segment, before its breakup to discontinuous droplets. Hydrodynamic instability theory, implemented in CFD codes, is often complemented by semi-empirical correlations for breakup length, which may limit parametric investigations. A basic mechanistic approach to the breakup length prediction, based on a simple momentum balance between the injected jet and the aerodynamic drag force due to the surrounding gas, which complements the classic hydrodynamic instability breakup mechanism, is suggested. This model offers a simple complementing mechanistic model. It is shown that obtained results compare well with published experiments, and with the established empirical correlation of Wu and Faeth (1995). A simplified version of the model, taking into account an inviscid hydrodynamic model is shown to maintain plausibility of breakup length predictions in fuel-injection relevant conditions.

Fuel injector performance has a direct effect on the combustion efficiency, pollutant emissions and combustion instability of internal combustion engines. Liquid fuels are normally accelerated into an elevated combustion-chamber temperature to maintain a desirable homogeneous combustible mixture - liquid vapour and air. The accelerated jet breakup may be induced by cavitation, turbulent, hydrodynamic and aerodynamic forces interactions and variation in fluid properties. The absolute majority of studies have been devoted to the extensive study on some of the effects that cause jet instability and breakup, while others are still at their infant study. In particular, relatively few researchers have studied the combined effects of jet acceleration and non-isothermal condition on jet instability and breakup, despite its practical relevance in liquid fuel spray and combustion.

The theory of liquid fuel jet instabilities has been developed under several assumptions, which include the assumption that the jets breakup processes are isothermal. However, liquid fuels are normally injected into an elevated combustion-chamber temperature to maintain a desirable homogeneous combustible mixture - liquid vapour and air. Therefore, a new linear theory model is developed for the instability and breakup of non-isothermal liquid jets, with consideration of a spatially variation of surface tension along the liquid-gas interface. The spatial variation of surface tension is obtained through temperature-dependent surface tension and transient heat-transfer from the combusting gases to the liquid jet. The classical interface hydrodynamic breakup theory and solution of heat-transfer through semi-infinite medium are coupled through the surface tension gradient. The analytical model accounts for the non-isothermal effects on jet breakup.