Sean C. Garrick

Direct numerical simulation of nanoparticle coagulation in a temporal mixing layer via a moment method

Direct numerical simulations of coagulating aerosols in two-dimensional, incompressible, iso-thermal mixing layers are performed. The evolution of the particle field is obtained by utilizing a moment method to approximate the aerosol general dynamic equation. We use a moment method which assumes a lognormal function for the particle size distribution and requires the knowledge of only the first three moments. This approach is advantageous in that the number of equations which are solved is greatly reduced. A Damkohler number is defined to represent the ratio of convection to coagulation time scales. Simulations are performed for three flows: Damkohler numbers of 0.2, 1, and 2. The spatio-temporal evolution of the first three moments along with the mean diameter and standard deviation are discussed.

Heat transfer - A review of 2001 literature

2. Conduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1892 2.1. Contact conduction and contact resistance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1892 2.2. Micro/nanoscale thermal effects, laser pulse heating, and hyperbolic heat transport . . 1892 2.3. Composites, heterogeneous media and complex geometries . . . . . . . . . . . . . . . . . . . 1893 2.4. Conduction with convection, phase change . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1893 2.5. Analytical, numerical and experimental studies . . . . . . . . . . . . . . . . . . . . . . . . . . . 1893 2.6. Thermomechanical problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1893 2.7. Miscellaneous and special applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1893

Nanoparticle Coagulation in a Planar Jet

Direct numerical simulation of nanoparticle coagulation in a planar jet is performed. The particle field is represented using a sectional method to approximate the aerosol general dynamic equation. The methodology is advantageous in that there are no a priori assumptions regarding the particle size distribution and coupled with an unsteady Navier-Stokes solver, it provides the spatio-temporal evolution of the particle field in an accurate manner. The jet consists of an incompressible fluid containing particles 1 nm in diameter issuing into a particle-free coflowing stream. Ten sections are solved allowing the particle field to develop to 8 nm in diameter. Results show that the geometric standard deviation reaches the self-preserving value within one jet diameter downstream of the nozzle and remains at that value up to 7.5 jet diameters. In this proximal region, the particle size is relatively uniform throughout the jet. Further downstream, the effects of large-scale vortical structures is to increase the residence time of particles within the domain and perturb the geometric standard deviation beyond the self-preserving value.

Large Eddy Simulation of Scalar Transport in a Turbulent Jet Flow

Large eddy simulation (LES) of turbulent reacting flows has been the subject of widespread investigation (McMurtry et al., 1992: Galperin and Orszag, 1993; Menon et al., 1993; McMurtry et al., 1993; Gao and O’Brien, 1993; Madnia and Givi, 1993; Frankel et al., 1993; Cook and Riley. 1994; Givi, 1994; Fureby and Lofstrom, 1994; Moller et al., 1996: Branley and Jones, 1997; Cook et al., 1997; Jimenez et al., 1997: Mathey and Choilet, 1997; Colucci et al., 1998; DesJardin and Frankel, 1998: Jaberi and James. 1998; Reveillon and Vervisch, 1998; Vervisch and Poinsot, 1988). Amongst these, recently Colucci et al. (1998) developed a methodology, termed the “filtered density function” (FDF). The fundamental property of the FDF is to account for the effects of subgrid scale (SGS) scalar fluctuations in a probabilistic manner. This is similar to probability density function (PDF) methods which have proven to be very useful in Reynolds averaging procedures (Libby and Williams, 1980; Libby and Williams. 1994: O’Brien. 1980; Pope, 1985; Dopazo, 1994). Colucci et al. (1998) developed a transport equation for the FDF in constant density flows in which the effects of unresolved convection and subgrid mixing are modeled similarly to those in “conventional” LES, and Reynolds averaging procedures. This transport equation was solved numerically by a Lagrangian Monte Carlo procedure and the results were compared with those obtained by direct numerical simulation (DNS) and by a conventional finite difference LES in which the effects of SGS scalar fluctuations are ignored (LES-FD).

The effects of turbulence on nanoparticle growth in turbulent reacting jets

The effects of turbulence on nanoparticle growth in turbulent reacting flows are studied via a priori analysis of direct numerical simulation data. The formation and growth of titanium dioxide nanoparticles in incompressible planar jets are simulated via gas-phase hydrolysis of titanium tetrachloride. The particle field is captured by utilizing a nodal approach which accounts for nucleation,condensation, and Brownian coagulation. Simulations are performed at a single Reynolds number and two different precursor concentration levels. Instantaneous, filtered, and averaged data are presented to convey the nature of turbulent or unresolved contributions to the growth of nanoparticles. The effects of turbulence on particle dynamics, in the context of both Reynolds-averaged Navier–Stokes simulation and large-eddy simulation, are assessed by comparing the exact, turbulent, and subgrid-scale growth rates. The results show that large particles are produced in the regions away from the jet core, and an increase in the precursor concentration level increases the particle mean diameter. Particles grow faster when the precursor concentration is increased. It is further observed that the growth rate of the particles is higher inside the eddies and it increases as the jet grows. Additionally, the results show that the unresolved small-scale fluctuations can both augment and inhibit particle growth. However the predominant effect is to reduce particle growth. This tendency is increased (in magnitude) as the precursor concentration level is increased.

Direct numerical simulation of nanoparticle coagulation in a temporal mixing layer

Direct numerical simulations of coagulating aerosols in two-dimensional, mixing layers are performed. The flows consist of the mixing of a particle-laden stream with a particle-free stream, with and without the presence of a temperature gradient. The evolution of the particle field is obtained by utilizing a sectional model to approximate the aerosol general dynamic equation. The sectional model is advantageous in that there are no a priori assumptions regarding the particle-size distribution. This representation facilitates the capture of the underlying physics in an accurate manner. The growth of particles between d p =1nm and d p =10 nm is captured in both isothermal flows and flows with a temperature gradient. Results indicate a reduced growth rate in the core of the eddy. The increased temperature of the particle-laden stream results in an increased growth rate. The growth and stretching of the surface area separating the two streams prevents the particle field from achieving the self-preserving particle-size distribution.

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

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.

Nanoparticle Coagulation in a Temporal Mixing Layer Mean and Size-selected Images

AbsractDirect numerical simulation of nanoparticle coagulation in a two-dimensional mixing layer is performed. A sectional model is used to discretize the particulate field resulting in a set of coupled non-linear partial differential equations each representing the concentration of particles of a particular size. The advantage of this approach is that it provides a robust mathematical framework for considering the particulate field as a function of space, time, and size with no apriori assumptions. The spatio-temporal evolution of the particulate field is visualized via the mean particle diameter and also in a size-specific manner.

Effects of Turbulent Fluctuations on Nanoparticle Coagulation in Shear Flows

The effects of fluid turbulence on the coagulation of aerosols are studied quantitatively and qualitatively. Direct numerical simulation data is used to isolate the effect of the small or subgrid-scale (SGS) particle–particle interactions on nanoparticle coagulation in three-dimensional flows. The rate of particle growth is decomposed into the contribution of the large-scales and small-scales interactions. The contribution of the small-scale interactions is presented as a function of time, space, flow dynamics, and coagulation Damköhler number. Results show that small-scale interactions act to both increase and decrease particle growth. The probability density functions (PDFs) of the SGS growth rate exhibit a negative bias, which increases with time and coagulation Damköhler number. Additionally, PDFs conditioned on the Q-criterion suggest that the contribution of the small-scale interactions primarily act to reduce particle growth in regions characterized by fluid rotation.

The Effects of Differential Diffusion on Nanoparticle Coagulation in Temporal Mixing Layers

The effects of size-independent diffusive transport on nanoparticle growth is studied by performing direct numerical simulation of nanoparticle coagulation in temporal mixing layers. The flow field is obtained by solving the incompressible Navier-Stokes equations, while the evolution of the particle field is obtained by using a nodal approach to approximate the aerosol general dynamic equation. Simulations are performed where particles diffuse according to their size and also where all particles have the same diffusivity. For the latter, the model assumes that all particles of different sizes have the same diffusivity as the smallest particles. The advantage of the second approach is the length scales that need to be resolved are larger, facilitating more affordable computations. Simulations are performed at two volume fractions to assess the effects of the models under different growth rates. The results indicate the use of size-independent diffusion coefficients predicts particle sizes and geometric standard deviations that are larger than those obtained with size-dependent diffusion coefficients.