Method of Moments Solutions for a Laminar Flow Aerosol Reactor Model

Abstract

This study compares the capabilities of the conventional and quadrature methods of moments to describe condensational growth in a well-known laminar ow aerosol reactor model. Governing equations for energy, lower order radial moments of the particle size distribution, and vapor transport are written for a twodimensional model using both approaches.Conventional and quadrature techniques to obtain closure of the moment equations are applied and compared. The conventional method requires certain approximations to the growth law. These include assumptions that the Kelvin effect is negligible and that the particle growth rate function is linear in particle size. In contrast, restrictive constraints of the conventional method of moments to obtain closure are avoided by applying the quadrature method. Numerical results for the laminar ow aerosol reactor model are obtained for a six moment formulation of the seed particle distribution to illustrate application of the quadrature method to continuous polydisperse distributions. We present the rst calculations with the new quadrature method of moments to a two-dimensional aerosol transport and growth model.

Nanoparticle coagulation via a Navier–Stokes/nodal methodology: Evolution of the particle field

“…This expense is compounded by the size-dependent diffusion coefficient, D k . Moment-based methods offer solution methodologies which are more computationally affordable but they are not as general as the nodal approach (McGraw, 1997;Terry et al, 2001;Wright et al, 2001Wright et al, , 2002. This generality, admittedly, comes with longer compute-times, as will be shown later.…”

“…The advantage of the nodal approach, in comparison to the sectional, is the great simplification of the integrals appearing in the coagulation/growth terms; these are reduced to sums in the nodal approach but require costly numerical integration in the sectional approach. Nodal/sectional methods are advantageous in that there are no a priori assumptions regarding the nature of the particle size distribution and they do not suffer from the severe constraints of other methodologies such as moment methods Seigneur et al, 1986;Zachariah & Semerjian, 1989;McGraw, 1997;Wright, McGraw, & Rosner, 2001;Terry, McGraw, & Rangel, 2001;Settumba & Garrick, 2003). In this work we consider particles between 1 and 12.7 nm in diameter, those typically consisting of thousands of molecules.…”

A comparison of diffusive transport in a moment method for nanoparticle coagulation

“…That is, a di usion coe cient which is based on the geometric mean particle volume is used for all particles independent of size (Moody & Collins, 2003). The results are compared to simulations in which particles di use according to their size (Pratsinis & Kim, 1989;Terry, McGraw, & Rangel, 2001;Suh, Zachariah, & Girshick, 2002;Settumba & Garrick, 2003). The e ects of di usion on the mean particle size, and geometric standard deviation are investigated for two initial volume fractions.…”

Nanoparticle coagulation in a planar jet via moment method

“…The combination of the DNS with the MM can provide the insights into the relationship between the fluid flow, particle properties and collision kernels [18] . However, the number of computational grid points needed is order of Re 9/4 in order to resolve all scales of fluid motion, which causes a heavy computational cost and can be prohibitively expensive computationally when the Re number is high.…”