Gradient theory modeling of transient transcritical phase transition of hydrocarbon fuel droplets

When subcritical fuel is injected into a supercritical environment, transcritical phase transition may occur, which serves as a fundamental problem in advanced combustion engines. In this work, gradient theory modeling of transient transcritical phase transition of hydrocarbon fuel droplets is performed under various ambient conditions. Results show that the evaporative mass transfer and the temporal evolution of liquid-gas interfacial stability jointly determines the phase transition pathway. Under supercritical ambient conditions, the rapid increase of interfacial temperature reduces the liquid-gas density contrast and weakens the thermodynamic non-uniformity across the interface. This leads to a sharp decrease in the grand-potential density difference and the tangential-pressure depression relative to the equilibrium pressure, thereby driving surface tension decay and the transition from a sharp liquid-gas interface to a diffuse mixing layer. The transient characteristics of the interface is largely affected by the ambient temperature, pressure, and fuel vapor mass fraction. Specifically, the ambient temperature accelerates heat and mass transfer, the ambient pressure enhances gas dissolution and promotes interfacial thickening, while the ambient fuel vapor is capable of suppressing subcritical evaporation yet promoting transcritical mixing at elevated temperature and pressure. Finally, a phase transition criterion is proposed based on the residual liquid-core mass ratio, showing good agreement with the phenomenological classification obtained from experimental results.