On the Use of Fractional-Order Quadrature-Based Moment Closures for Predicting Soot Formation in Laminar Flames

ABSTRACT

The accurate numerical prediction of soot formation in practical combustion devices remains a challenge. Several new quadrature-based moment closures based on fractional-order moments of soot particle volume are proposed for the prediction of soot formation in laminar diffusion flames at atmospheric and elevated pressures. Both univariate Quadrature Method of Moments (QMOM) models based on a classical particle volume formulation and bivariate Conditional Quadrature Method of Moments (CQMOM) models based on a new particle volume/primary particle number formulation are proposed. The soot models include detailed gas-phase chemistry along with nucleation, surface growth, oxidation, and coalescence/coagulation soot chemistry source terms. Initial comparisons to predictions of a sectional method for space homogeneous simulations illustrate well the improved predictions of soot number density and volume fraction are provided by the fractional-order moment closures compared to integer-order moment approaches. Furthermore, additional comparisons of soot prediction of methane/ethanol laminar diffusion flames at elevated pressures indicate that the proposed bivariate CQMOM, with a specified soot inception size, offer significantly improved results when compared to the other variants and available experimental data.

KEYWORDS:

• Soot
• soot modeling
• method of moments
• QBMM
• CQMOM
• CQMOM-Radau
• ethanol
• laminar diffusion flames

Acknowledgments

This research was funded by grants and contracts from the Green Aviation Research and Development Network (GARDN), Southern Ontario Smart Computing for Innovation Platform (SOSCIP), as well as Pratt & Whitney Canada. The first author also received support in the from of a scholarship from the Natural Sciences and Engineering Research Council (NSERC) of Canada. Additionally, the computational resources for performing the numerical simulations reported herein were provided by the SOSCIP program as well as the SciNet High Performance Computing Consortium at the University of Toronto and Compute/Calcul Canada (the latter are funded by the Canada Foundation for Innovation (CFI) and Province of Ontario, Canada).