An Eulerian CFD study for aerosol formation in a turbulent jet using the sectional method and a size-dependent particle surface tension

Abstract

An Eulerian aerosol dynamics and transport model embedded in a general-purpose Computational Fluid Dynamics (CFD) code is presented. The model employs the sectional method for the representation of the particle size distribution and a recently developed method for the numerical solution of growth that efficiently tackles numerical diffusion. The model is used for the simulation of the experiments of (K. Lesniewski & Friedlander, 1998) on homogeneous nucleation of dibutylphthalate (DBP) in a free turbulent jet. Different URANS models, including the recent STRUCT-$\epsilon$ model, as well as LES are used. In previous simulation studies, the spatial distribution of particle formation along the jet was reproduced by arbitrarily altering the bulk surface tension formula, an aspect that was also verified by the present simulations. In this study, however, the selection of turbulence model, notably the RNG $k$-$\epsilon$ model, was found to have a similar effect, implying that the flow, heat and vapor transport modelling may have a similar effect on the qualitative prediction of the spatial structure of nucleation. Attempting to overcome the limitations of the capillarity assumption in the Classical Nucleation Theory (CNT), a new modification of the nucleation rate formula is derived, considering a surface tension dependent on the particle size by using the Tolman length concept. This modification, with a Tolman length equal to 0.25 nm or 0.325 nm, depending on the formula for the bulk liquid surface tension for DBP, allowed the model to accurately predict the slope of the dependence of the formed particle concentration on the vapor inlet supply, which was not correctly reproduced in the previous studies. The successful use of a widespread CFD code expands significantly the pool of available computational tools for studying nucleation. Nevertheless, the conclusion of previous works that the specific experiments are difficult to simulate is also reiterated, implying that further research is needed not only to understand the limitations of the nucleation theory and their quantitative impact, but also to qualitatively predict the characteristics of the spatial structure of nucleation and condensation in turbulent aerosol flows.