Lowering diesel engine emission levels, while preserving performance, is the main demand in the development of current and future diesel engines. To fulfill it, the in-cylinder vaporization and combustion processes of the diesel spray must be well understood. An important parameter in the vaporization process of a diesel spray is the maximal penetration distance of liquid fuel (i.e. the "liquid length"). So-called mixing-limited vaporization models assume that the vaporization rate of the fuel is limited by the mixing rate of fuel and ambient gas. Such models have been shown in the literature to accurately correlate liquid lengths for moderate to high in-cylinder densities, i.e. in the density range relevant to modern diesel engines. Since in-cylinder pressures can reach high absolute levels, real gas effects should be considered in these models. Critical evaluation of the most commonly used mixing-limited vaporization model (Siebers, SAE 1999-01-0528) reveals that real gas effects are not implemented consistently, since compressibility factors of the fuel and ambient gas are decoupled.In this work the Siebers model is adapted to properly include real gas effects, using saturated vapor fractions from equilibrium flash calculations based on the Peng-Robinson equation of state. Results of the original and revised models are compared to experimental liquid length data from Sandia National Laboratories for various fuels, densities and temperatures. At relatively low ambient densities, the original and revised models give identical results, as expected. At higher densities, more relevant to current and future diesel engines, the difference becomes significant. Moreover, liquid lengths computed with the revised model are closer to experimental data, especially at the highest ambient pressures. It is concluded that the overall predictive capability of the Siebers model can be improved using the method to include real gas effects presented here.
Kurvers, C., & Luijten, C. C. M. (2010). Real gas effects in Siebers’ mixing-limited spray vaporization model. SAE International Journal of Engines, 2010-01-1497-1/9. https://doi.org/10.4271/2010-01-1497