A scaling law for the maximum penetration distance of liquid-phase fuel in a diesel spray (defined as the liquid length) was developed by applying jet theory to a simplified model of a spray. The scaling law accounts for injector, fuel, and in-cylinder thermodynamic conditions on liquid length, and provides significant insight into the fuel vaporization process. As developed, the scaling law is valid for single-component fuels, but can be used to model multi-component fuels through use of single-component surrogate fuels.
Close agreement between the scaling law and measured liquid length data over a very wide range of conditions is demonstrated. The agreement suggests that vaporization in sprays from current-technology, direct-injection (DI) diesel injectors is limited by mixing processes in the spray. The mixing processes include entrainment of high-temperature air and the overall transport and mixing of fuel and air throughout the spray cross-section. An implication of mixing limited vaporization is that the processes of atomization and the ensuing interphase transport of mass and energy at droplet surfaces are not limiting steps with respect to fuel vaporization in DI diesel sprays.
The scaling law provides a fundamental baseline on liquid fuel penetration and vaporization in diesel sprays that can be compared with the vaporization aspects of the multi-dimensional diesel spray models under development. The scaling law can also provide design guidance on the expected maximum extent of liquid-phase fuel penetration in engines. Application of the scaling law to a heavy-duty and a light-duty DI diesel shows that liquid-phase fuel impingement on piston bowl walls is not a serious concern in heavy-duty engines using a typical diesel fuel, as observed previously through experiments, but may be an issue in light-duty engines.