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

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.