Modeling of aerosol formation in a turbulent jet with the transported population balance equation-probability density function approach

Abstract

Processes involving particle formation in turbulent flows feature complex interactions between turbulence and the various physicochemical processes involved. An example of such a process is aerosol formation in a turbulent jet, a process investigated experimentally by Lesniewski and Friedlander [Proc. R. Soc. London, Ser. A 454, 2477 (1998)]. Polydispersed particle formation can be described mathematically by a population balance (also called general dynamic) equation, but its formulation and use within a turbulent flow are riddled with problems, as straightforward averaging results in unknown correlations. In this paper we employ a probability density function formalism in conjunction with the population balance equation (the PBE-PDF method) to simulate and study the experiments of Lesniewski and Friedlander. The approach allows studying the effects of turbulence-particle formation interaction, as well as the prediction of the particle size distribution and the incorporation of kinetics of arbitrary complexity in the population balance equation. It is found that turbulence critically affects the first stages of the process, while it seems to have a secondary effect downstream. While Lesniewski and Friedlander argued that the bulk of the nucleation arises in the initial mixing layer, our results indicate that most of the particles nucleate downstream. The full particle size distributions are obtained via our method and can be compared to the experimental results showing good agreement. The sources of uncertainties in the experiments and the kinetic expressions are analyzed, and the underlying mechanisms that affect the evolution of particle size distribution are discussed.

An explicit adaptive grid approach for the numerical solution of the population balance equation

“…Here, the semi-discrete system consists of scalar transport equations for so-called discrete number densities. Since these transport equations are formally identical to those of the reactive scalars which characterize the fluid phase, the PBE can be naturally incorporated into models for the laminar or turbulent carrier flow [8,9,34,35].…”

An LES-PBE-PDF approach for modeling particle formation in turbulent reacting flows

“…Campos and Lage [9] pointed out that, strictly, DPBs are not function approximation methods and that the particle size distribution hence converges slower than its moments as the number of bins is increased. This is at variance with direct discretization approaches such as finite volume [72] or finite element methods [12,13]. Here, however, both the particle property distribution and all of its moments are affected by a discretization error [63].…”

“…For the same experimental campaign, Di Veroli and Rigopoulos [13] argued that, in the course of the measurements, droplet formation may have continued in the sampling tube, accounting, in part, for the mismatch between measured droplet size distributions and RANS-PBE-PDF predictions. Recently, Neuber et al [47] concluded that, in the presence of kinetic and experimental uncertainties, a quantitative model validation may instead be based on a series of experiments covering different operating conditions.…”

“…The main advantage of the so-called PBE-PDF method is that it allows for the prediction of the particle property distribution and is able to accommodate any fluid or particle phase kinetics without approximation. This was first demonstrated by Di Veroli and Rigopoulos [11,12,13] who considered the RANS turbulence model and validated PBE-PDF predictions for a finite element discretization of the particle size distribution in two experimental test cases. Additionally, they were able to show that a numerical solution of the joint scalar-discrete number density pdf transport equation is computationally viable and can be achieved in reasonable computing times by using a Lagrangian stochastic particle solver [53].…”

“…The particular adaptive grid scheme which we apply is able to accurately resolve sharp moving features of the particle property distribution and, for a given accuracy, requires about an order of magnitude fewer grid points in particle property space than its fixed grid counterparts [12,13].…”