Large Eddy Simulation of the evolution of the soot size distribution in turbulent nonpremixed flames using the Bivariate Multi-Moment Sectional Method

A joint volume -surface formalism of the Multi -Moment Sectional Method (MMSM) is developed to describe the evolution of soot size distribution in turbulent reacting flows. The bivariate MMSM (or BMMSM) considers three statistical moments per section, including the total soot number density, total soot volume, and total soot surface area per section. A linear profile along the volume coordinate is considered to reconstruct the size distribution within each section, which weights a delta function along the surface coordinate. Closure for the surface area as a function of volume within each section is achieved by assuming that the primary particle diameter so surface/volume ratio is constant within each section. The inclusion of the new surface area variable in BMMSM allows for the description of soot's fractal aggregate morphology compared to the strictly spherical assumption of its univariate predecessor. BMMSM is shown to reproduce bimodal soot size distributions in simulations of one-dimensional laminar sooting flames as in experimental measurements. To demonstrate its performance in turbulent reacting flows, BMMSM is coupled to a Large Eddy Simulation (LES) framework to simulate a laboratory -scale turbulent nonpremixed jet flame, demonstrating the feasibility of using a sectional -like approach with an inherently bivariate soot model in LES. Computational results are validated against available experimental measurements of soot size distribution, showing the ability of BMMSM to reproduce the evolution of the size distribution from unimodal to bimodal moving downstream in the flame. In general, varying the number of sections has limited influence on results, and accurate results are obtained with as few as eight sections so 24 total degrees of freedom. The impact of using a different statistical model for soot such as the Hybrid Method of Moment (HMOM) is also investigated. Aside from the fact that HMOM cannot provide information about the soot size distribution, the most significant qualitative difference between HMOM and BMMSM is in number density in the oxidation region of the flame, suggesting that BMMSM outperforms HMOM in reproducing key aspects of the soot oxidation process. Finally, the total computational cost of using BMMSM is as low as approximately 44% more than the cost of HMOM. Therefore, the new formulation results in a computationally efficient approach for the soot size distribution in turbulent reacting flows, enabling simulations of the soot size distribution in complex industrial configurations that are unattainable using traditional sectional models. Novelty and Significance Statement This paper introduces a joint volume -surface formulation of the Multi -Moment Sectional Method (MMSM), called the bivariate MMSM (BMMSM), which allows for tracking the soot size distribution in turbulent reacting flows including soot's fractal aggregate morphology. Also, this model has been implemented in a Large Eddy Simulation framework, which allows for the description of the evolution of the soot size distribution in turbulent combustion. BMMSM is shown to qualitatively and quantitatively predict the evolution of the soot size distribution in laminar and turbulent flames. Overall, the total computational cost for turbulent reacting flows is only marginally more (44%) than the cost of traditional moment methods, which do not provide the soot size distribution.