This paper presents a numerical framework for characterizing fuel injection in modern combustors. The approach utilizes scaling analysis to describe the droplet evaporation in non-dimensional and fluid-independent terms. The results of the model are validated against published experimental data of isolated droplets evaporating at subcritical and near-critical conditions. The model is incorporated in a spray calculation framework and extended to the supercritical regime to assess the impact of different fluid-properties and evaporation models on temperature and fuel vapor distributions.
The results suggest that in a non-convective environment the transient and quasi-steady evaporation rates vary exponentially with Lewis number. Furthermore, the results show fluid-independent behavior of the droplet evaporation, indicating that a single-component fluid can potentially be used as a modeling surrogate for jet fuel. The first-principles analysis demonstrates that classical evaporation models overestimate transient evaporation and underestimate quasi-steady evaporation, with discrepancies up to 70% at supercritical conditions. This is due to limitations in fuel-property description and the lack of non-isothermal droplet characterization at near-critical conditions. The temperature profiles are typically under-predicted and fuel vapor concentrations are over-predicted in standard spray calculations with subcritical evaporation models. As such the proposed framework breaks new ground in modeling of supercritical fuel injection. The improved quality in the predicted fuel concentration and temperature distribution can enable more accurate assessment of flame position, improving the estimation of combustion stability margins and NOx emissions. The model can be incorporated in commercial codes to guide the design of combustors operating at supercritical conditions.