Detailed modeling of soot particle formation and comparison to optical diagnostics and size distribution measurements in premixed flames using a method of moments

Recently improved knowledge about key processes for the formation and growth of soot particles lead to very extensive soot models describing several kinetic pathways for particle nucleation and growth in detail. One of these models has been proposed by D'Anna and coworkers (D'Anna et al., 2010, Sirignano et al., 2010). In these original studies, the multivariate formulation was solved with a sectional approach, while a more recent study (Salenbauch et al., 2017) also showed the suitability of moment methods such as the Conditional Quadrature Method of Moments (CQMOM) (Yuan et al., 2011). However, being a moment method, CQMOM does not allow to directly access the soot particle size distribution (PSD). This prevents the consistent comparability of CQMOM results to soot measurements based on a scanning mobility particle sizer (SMPS). Furthermore, the comparison to laser-induced fluorescence (LIF) experiments is also limited, as the LIF signal only represents small particles and their concentration is only extractable from the simulation results if the PSD shape is known. The aim of this study is to extend the previously developed CQMOM soot model by a PSD reconstruction step applying the concept of entropy maximization. Maintaining the efficiency of the CQMOM moment inversion algorithm to close the moment equations, the model extension enables to evaluate the diameter-based PSD in a post-processing step without prescribing a specific shape as input. The updated algorithm is applied to simulate soot formation in two different burner-stabilized premixed C2H4/O-2/N-2 flames with a very lightly sooting (C/O = 0.67) and a heavily sooting (C/O= 0.77) character. Numerical results are compared to recently published LIF, laser-induced incandescence (LII) and SMPS measurement data. The analysis investigates the model's capability to predict phenomena such as uni-or bimodal distribution shapes and the transition of small nanostructures to agglomerates in the two target flames both of which exhibit very different sooting behaviour.