An Analytical Energy-budget Model for Diesel Droplet Impingement on an Inclined Solid Wall

The study of spray-wall interaction is of great importance to understand the dynamics that occur during fuel impingement onto the chamber wall or piston surfaces in internal combustion engines. It is found that the maximum spreading length of an impinged droplet can provide a quantitative estimation of heat transfer and energy transformation for spray-wall interaction. Furthermore, it influences the air-fuel mixing and hydrocarbon and particle emissions at combusting conditions. In this paper, an analytical model of a single diesel droplet impinging on the wall with different inclined angles (α) is developed in terms of β_m (dimensionless maximum spreading length, the ratio of maximum spreading length to initial droplet diameter) to understand the detailed impinging dynamic process. This analytical model is built up based on the energy conservation that considers kinetic energy, gravitation energy, and surface energy before impingement, as well as viscous dissipation, gravitation energy, adhesion energy, and deformation energy after impingement. The experimental work of diesel droplet impinging on an inclined wall is performed at a certain range of the impact Weber number (We of 33 to 420) with various inclined angles (α of 0 to 45°) to study the effects of the inclined angle on the temporal evolution of the post-impingement characteristics (i.e. droplet spreading length, dynamic contact angle). The analytical model is validated and evaluated at the aforementioned experimental operating points. The validated model is further utilized to determine the transition between capillary region and kinetic region at different inclined angle of the wall.