Development of similarity and normalization models for spray characteristics with the momentum equation as the theoretical basis

Fuel atomization in diesel engines can be significantly improved by elevating the injection pressure and decreasing the nozzle orifice diameter. Addressing the limited research on mathematical modeling within the regime of 300-MPa-level injection and micro-holes, this paper presents a comprehensive study on the similarity and normalization of spray evolution for ultra-high-pressure micro-nozzle configurations. In the experiments, key parameters such as injection pressure difference, ambient density, and hole diameter were selected as the main variables. The spray development process was divided into two main stages, and the similarity criteria and normalization equations for spray characteristics were derived accordingly. Combined with the DBI (Diffused Back-Illumination) method and processing technology, experimental data were obtained to verify the reliability of the established models. The experimental results show that both the similarity conversion results and normalization results of the derived mathematical models exhibit good consistency with the experimental data. This study can provide theoretical support for the optimization and spray characteristic prediction of ultra-high pressure small high-speed diesel engines.