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Computational models widely employed for predicting the dispersion of fuel sprays in combustion engines suffer from well-known drawbacks associated with the utilization of case-dependent empirical phase-change models, describing the conversion of liquid into vapour during fuel injection. The present work couples the compressible Navier-Stokes and energy conservation equations with a thermodynamic closure approximation covering pressures from 25 to 2000bar and temperatures that expand from compressed liquid, vapor-liquid equilibrium to trans/supercritical mixing, and thus, cover the whole range of P-T values that diesel fuel undergoes during its injection into combustion engines. The model assumes mechanical and thermal equilibrium between the liquid, vapour and surrounding air phases and thus, it avoids utilization of case-dependent empirical phase-change models for predicting in-nozzle cavitation and vaporization of fuels.