Large Eddy Simulation of Titanium Dioxide Nanoparticle Formation and Growth in Turbulent Jets

Abstract

Large eddy simulations (LES) of titanium dioxide nanoparticles in three dimensional turbulent reacting planar jets are performed. The spatio-temporal evolution of the particle field is obtained by utilizing a nodal representation of the general dynamic equation. Gradient-diffusion, Smagorinsky-type subgrid-scale closures are employed to account for the unresolved stresses, fluid-scalar fluxes, and fluid-particle fluxes. The effect of the unresolved fluctuations on coagulation are neglected. Simulations are performed at two different precursor concentration levels. Comparison between results obtained via direct numerical simulation (DNS) and LES is performed to assess the performance of the closures. The LES performs fairly well in predicting the particle concentration as a function of size as well as the mean diameter. Additionally the polydispersity of the LES particle field is greater than that of the DNS. The results also suggest that at as the precursor concentration increases, neglect of the unresolved particle-particle interactions may act to increase the nanoparticle growth-rate.

Effects of Turbulent Fluctuations on Nanoparticle Coagulation in Shear Flows

“…Similarly the effect of the unresolved, small-scale interactions is more pronounced as Da increases. This trend has been observed in the LES of Loeffler et al 2011. The work showed that at higher precursor concentrations-which produces a greater number of…”

“…The filter-width is L = 2π/50 = 12 × DNS . The box filter is a popular choice in performing LES because of its computational simplicity, and the chosen filter width corresponds to a resolution typically used in LES of similar flows (Garrick 1995;Colucci et al 1998;Loeffler et al 2011). In addition to the total or exact growth rate defined above, we define a growth rate of the large, mean, or resolved scales M .…”

“…These are the scales which need to be accounted for when performing "turbulent simulations." For example, in LES, the large-scale dynamics are explicitly solvedfor, or resolved, while the small-scales dynamics are modeled (Smagorinsky 1963;De Stefano and Vasilyev 2002;Dong et al 2003;Kurose and Makino 2003;Loeffler et al 2011). This approach, when performed correctly, facilitates affordable and reliable computations (Givi 1989;Garrick 1995;Colucci et al 1998;Pope 2000;Sagaut 2001;Givi 2006).…”

“…Recently, the DNS of titania formation and growth (via the hydrolysis of titanium tetrachloride) showed that neglect of the small-scale interactions/fluctuations result in smaller particles (Das and Garrick 2010). Additionally, the LES of similar flows has shown a discrepancy between the "exact" and model results Loeffler et al 2011. To create accurate models for the unresolved, small-scale particle-particle interactions, their characteristics and effects must be better understood (Friedlander 2000;Reade and Collins 2000).…”

“…is computeintensive even for simple flows. When the small length-scales and short time-scales associated with fluid turbulence are present, direct numerical simulation (DNS) is often impossible and modeling of the underlying phenomena is required (Frish-man et al 1997;Tammet and Kulmala 2005;Albriet et al 2010;Wu and Menon 2001;Settumba and Garrick 2007;Loeffler et al 2011). Accurate and affordable computational tools-based on Reynolds-averaged Navier-Stokes simulations (RANS) or increasingly based on large-eddy simulation (LES)-are greatly needed (Marchisio and Fox 2005;Schwarzer et al 2006;Rigopoulos 2007).…”