Development of High Fidelity Soot Aerosol Dynamics Models using Method of Moments with Interpolative Closure

Abstract

The method of moments with interpolative closure (MOMIC) for soot formation and growth provides a detailed modeling framework maintaining a good balance in generality, accuracy, robustness, and computational efficiency. This study presents several computational issues in the development and implementation of the MOMIC-based soot modeling for direct numerical simulations (DNS). The issues of concern include a wide dynamic range of numbers, choice of normalization, high effective Schmidt number of soot particles, and realizability of the soot particle size distribution function (PSDF). These problems are not unique to DNS, but they are often exacerbated by the high-order numerical schemes used in DNS. Four specific issues are discussed in this article: the treatment of soot diffusion, choice of interpolation scheme for MOMIC, an approach to deal with strongly oxidizing environments, and realizability of the PSDF. General, robust, and stable approaches are sought to address these issues, minimizing the use of ad hoc treatments such as clipping. The solutions proposed and demonstrated here are being applied to generate new physical insight into complex turbulence-chemistry-soot-radiation interactions in turbulent reacting flows using DNS.

New scheme for implementing the method of moments with interpolative closure

“…For m 0 shown in Figure 2a, a less number of interpolation points leads to smaller relative errors, indicating the Runge phenomenon exists in the newly proposed MOMIC scheme. The Lagrange interpolation can cause Runge phenomenon, which has been reported by Roy et al (2014). In this section, the new MOMIC scheme with (H D 2, S D 3, f D 2) shows advantage in accuracy as compared to the Frenklach and Harris's MOMIC.…”

“…Population balance modeling (PBM) is increasingly popular in colloid and particulate process engineering (Frenklach 2002; Ramkrishna and Singh 2014; Hashemian and Armaou 2016; Raman and Fox 2016). The successful implementation of PBM entails two major aspects: first, the reliable numerical solution of the population balance equation (PBE), which determines the time evolution of particle size distribution because of internal dynamics including nucleation, condensation, and coagulation; second, the suitable coupling treatment between the PBE and Navier-Stokes equations in a Eulerian framework (Marchisio and Fox 2005;Wang et al 2005;Roy et al 2014). The numerical solution of PBE (i.e., the mathematical treatment of internal dynamics) is primarily important in these studies, determining whether or not the modeling can be reliably implemented.…”

“…The conclusions of this study are presented in Section 4. This article is limited to the solution of PBEs without considering its transport in flows, thus some key schemes, such as the preservation of realizability and monotonicity of the moment distribution (Vikas et al 2013;Roy et al 2014), were not included.…”

Modelling of Soot Aerosol Dynamics in Turbulent Flow

“…LES studies of turbulent combustion with soot have appeared in the last decade, mostly on laboratory flames [91, 93, 100-102, 137, 146, 172, 173], but recently also on IC engines [164] and gas turbine combustors [103,174]. Finally, there have been a few studies of sooting flames that use Direct Numerical Simulation (DNS) where no turbulence model is employed [175][176][177][178][179][180][181][182]. More details on these studies will be given in Section 6.2.…”

Direct numerical simulations of non-premixed ethylene–air flames: Local flame extinction criterion

“…[27] was employed to reduce the mechanism and remove any chemical stiffness, rendering it suitable to DNS application. It is noted that the reduced mechanism with PAH chemistry was first developed for DNS of sooting flames [28][29][30].…”