Modeling and simulation of homogeneous nucleation in turbulent flows: physics, methods and realizable solutions

Numerical simulations of nanoparticle nucleation in turbulent shear flows are performed. We consider the homogeneous nucleation of dibutyl-phthalate (DBP) nanoparticles via direct numerical simulation (DNS) and large-eddy simulation (LES). The flows consist of a high-temperature, DBP-laden stream issuing into a low-temperature, faster or slower moving, DBP-free environment. As the flows cool, via molecular and large- scale convective mixing, the DBP vapor becomes highly supersaturated and particles are formed by nucleation. This particle formation takes place in the absence of condensation or coagulation. Classical nucleation theory is used to model particle nucleation and the Navier-Stokes equations are coupled with the scalar transport equations to provide the fluid, thermal, and chemical fields.;The effects of large-scale mixing and vapor concentration on homogeneous nucleation rates are investigated via DNS in three-dimensional planar jets. The simulation results provide a demonstration of how nucleation takes place in narrow regions where molecular mixing of the two streams occurs. When maximum nucleation rates occur in conditions where the nucleation rates are sensitive to ambient conditions, islands of nucleation form. There are two possible nucleation events: initial shear layer nucleation, and later nucleation in coherent structures or eddies generated by the velocity difference between the jet and the co-flow. A scatter plot diagram of observed dilution paths in temperature versus condensable vapor concentration space where nucleation rates are superimposed is shown to be a convenient tool for analyzing nucleation events. Convection by large-scale eddies gradually spreads the range of mixing paths in this space towards higher nucleation rates. The results also show that boundary conditions, including inlet concentration and velocity ratio, have both qualitative and quantitative effects on particle nucleation. The effects of Lewis number on the homogeneous nucleation of DBP particles are also studied via DNS. Simulations at two Lewis numbers are performed to investigate the effects of molecular mixing on nucleation. These simulations are also carried out at two co-flow velocities to assess the effects of large-scale mixing. The results show that the Lewis number as well the level of large-scale mixing inherent in the flow have substantial effects on particle nucleation.;The effects of the subgrid-scale (SGS) scalar interactions on nanoparticle nucleation are investigated via a priori analysis of DNS data. To assess the effect of SGS scalar interactions on DBP particle nucleation, the temperature and mass-fractions are filtered and the resulting quantities are used to compute the nucleating particle field. Two filter widths are used to obtain varying levels of SGS interactions. Particle size distributions are computed to examine the particle fields produced. This work shows that the SGS interactions' effect on nucleation has two distinct trends. In the proximal region of the flow, the unresolved interactions act to decrease particle formation. However, as the flow transitions or becomes turbulent the effect of the SGS interactions acts to increase particle formation.;In the DNS, all relevant length and time-scales are resolved while in LES a closure is used to represent the SGS stress, and fluid-scalar fluxes. We perform the LES at two resolutions to illustrate the effect of "resolving less" and "modeling more". Additionally, to illustrate the effects of the SGS interactions on homogeneous nucleation in turbulent flows, the unresolved scalar-scalar interactions appearing in nucleation source term are neglected. The results again show that nucleation initially occurs in the shear layers where molecular transport dominates and across the span of the wake once the core collapses and the flow transitions to turbulence. Pre-transition, the saturation ratio - representative of the driving force for particle formation - predicted by the LES and DNS is quite similar. Post-transition, the saturation ratios predicted by the LES are significantly greater than those predicted by the DNS, and the discrepancy increases as the filter-width increases (and resolution decreases). This dynamic is also reflected in the nucleation rate. The LES predicts nucleation rates between one and two orders of magnitude greater than the DNS and the discrepancy increases as the resolution decreases. There is also a shift towards the nucleation of smaller nanoparticles in the LES compared to the DNS. The results suggests that the SGS interactions act to decrease the rate of nanoparticle nucleation and increase nuclei size. The compute time between the DNS and LES decreased by three orders of magnitude, suggesting that SGS closures for nucleation would be a significant addition to simulation capabilities and tools. The work concludes with a discussion of a probabilistic method able to resolve these issues, which are inherent to LES.