Systematic assessment of the Method of Moments with Interpolative Closure and guidelines for its application to soot particle dynamics in laminar and turbulent flames

Abstract

The Method of Moments with Interpolative Closure (MOMIC) is a widely used approach for numerical modeling of aerosol dynamics, where soot formation is an important area of application. Two basic variants of the algorithm were proposed in the past: In the original method, transport equations are solved for several non-negative order integer moments of the soot Number Density Function and one for the moment of order minus infinity. Based on these moments, two interpolation functions are constructed and used for the evaluation of positive and negative fractional order moments required for closure of the moment equation source terms. In the other variant, which is a simplification of the first, equations are solved only for non-negative order integer moments. Negative order moments then need to be evaluated by extrapolation. In addition to the choice between these two algorithms, it is not clear a-priori what is the optimal choice regarding the number of transported moments and hence the order of the interpolation polynomial. In this work, the effects of different choices in the setup of the MOMIC algorithm on the evaluation of soot source terms and the prediction of the soot number density and volume fraction are assessed systematically. To this end, MOMIC is combined with a state-of-the-art physico-chemical soot model and applied to the simulation of soot formation in a laminar premixed flame and along Lagrangian trajectories extracted from a Direct Numerical Simulation of a turbulent sooting flame. Monte Carlo simulations serve as reference solutions for a combined a-priori and a-posteriori study. Including the moment of order minus infinity is shown to be beneficial for an accurate calculation of the coagulation source term and hence the soot number density, because moments of negative order can be evaluated more accurately. Furthermore, a high interpolation order yields a more accurate prediction of the surface growth source term. This source term is systematically overpredicted, but errors are substantially reduced to a few percent with increasing interpolation order.