One-dimensional model on liquid-phase fuel penetration in diesel sprays

• A one-dimensional model was developed for predicting liquid length of diesel spray.
• The radial velocity and fuel volume fraction distribution are taken into considered.
• The velocity and fuel concentration profiles are treated as a Gaussian radial distribution function.
• Effect of distribution factor (β) on the prediction of liquid length is studied.

This paper reports a theory investigation focusing on liquid penetration of diesel spray. A one-dimensional model on liquid length is developed for the prediction of liquid length, based on the momentum flux and fuel mass flux conservation along the sprays' axis, and energy conservation on the control volume. The heterogeneous distribution of velocity and fuel concentration over the cross-section of spray is taken into consideration. A Gaussian radial profile is assumed for the velocity and fuel volume fraction distribution, and a distribution factor (β) is introduced to describe the distribution profile of axial velocity and fuel volume fraction. The model derived in this research was validated by the measured data from Siebers' experiment over a wide ambient gas temperature and density. This comparison indicates that the velocity and fuel concentration profiles are critical and cannot be neglected in the derivation of liquid length. The distribution factor is confirmed from the best fit of the calculated liquid lengths to the measured data, and should be set as 1.8 for the best fit. The model is further validated by the measured data over a wide orifice pressure drop, orifice diameter, and fuel temperature range. Based on the validated model, liquid length of diesel spray under different gas composition is calculated, and effect of ambient gas composition on liquid length is discussed.