The general formulation of the energy equation and the impact of enthalpy diffusion on multi-component droplet heat and mass transfer

Abstract

A key aspect of modeling the heat and mass transport of droplets is the description of diffusion transport, and multiple approaches exist to address it. While many contributions focus on the description of the mass transfer, details about the energy formulation to describe the droplet’s heat transfer are seldom developed in the literature. This work demonstrates that a general gas-phase energy formulation can be obtained independently from the species diffusion transport modeling while incorporating multi-species enthalpy diffusion terms with a simple expression. Considering the ideal gas simplification, it is shown that a simple choice of specific heats is sufficient to characterize the inclusion or not of multi-species enthalpy diffusion effects. Furthermore, it is also demonstrated that the final energy expression degenerates in the single-component limit to the same energy formulation as in the model of (Abramzon and Sirignano, Int. J. Heat and Mass Trans, Vol.32(9), pp.1605–1618, 1989), considered as a reference in the literature. Simulations are conducted for droplets of multiple fuel compositions in varied atmospheric conditions to represent spray combustion scenarios and evaluate the impact of incorporating or not the enthalpy diffusion term, and conclude on the need and ease of use of the proposed energy formulation.