Study of droplet dynamics in transcritical environments

Abstract

Efficient combustion processes are indispensable in limiting the temperature increase to 1.5 deg C as set by Intergovernmental Panel on Climate Change (IPCC) before 2030 to curtail the effects of global warming. As for the emissions, the main task lies in controlling the air-fuel ratio in the lean regime as to control the emissions of NOx since they reach maximum discharge at the stoichiometric ratio whereas improper mixing can lead to an increase in CO emissions. Thus, the air and fuel interactions need to be studied to achieve control over emissions. To that end, good computational models are necessary to supplement the design process to control both the emissions and combustion instabilities. The latter can severely damage the combustion chamber. Therefore, the proper modeling of the fuel-air interfaces in high-pressures is pivotal as they differ significantly from the low-pressure injection. Various numerical droplet evaporation models are studied in trans/supercritical environments, the fluid is called supercritical when it's above the critical states whereas it is called transcritical when it passes the critical state. As for the droplets, two components were selected namely n-heptane and n-dodecane. The former for 0-D and 1-D models and the latter for 3-D models, the cases were dictated by the availability of experimental works. As for the 0-D and 1-D models, various correlations based on the Nusselt and Sherwood numbers were utilized. The Prandtl number and other non-dimensional numbers were computed by thermophysical property models based on the 1/3 rd rule rather than fixed values. In comparison, the developed 0-D and 1-D models conform to the experimental results and other computational studies ranging from perfect-gas to real-gas against the experimental work available in the literature. It is hypothesized that the differences in the computation of the latent heat of vaporization are more pronounced in the accuracy of the lifetime of the droplet rather than the density of the components. In 3-D models, the liquid-vapor interface is modeled by level-set and phase-field methods. Thermodynamic closure is achieved by the Peng- Robinson equation of state. Prandtl number assumption model is invoked for the computation of the liquid thermal conductivity, Chung model for the calculation of viscosity of mixtures, and Firoozabadi model for the Maxwell-Stefan diffusion coefficient. A basic model is used for the computation of surface tension coefficient for the phase-field 3-D models. A qualitative agreement was observed between the 3D model under this study, numerical work, and the experimental campaign of microscopic droplets for all the three vaporization regimes namely classical, translational and diffusive mixing. All the models yielded olive-shaped droplets. Effects of mesh resolution on the phase-field quantities were studied and contrasted with the same mesh size for the level set method in a 2-D configuration. Recommendations include better surface tension models, thermal conductivity for gaseous mixtures, the inclusion of PC-SAFT equation of state, cross-diffusion terms, and high mesh resolution of the O(-7) m in the droplet region coupled with adaptive meshing based on the gradient of the phase-field parameter.