The numerical simulation of the soot particle size distribution in flames is addressed by solving the balance equations for total number density and the probability density function of particle sizes, leading to a hybrid stochastic/fixed-sectional method for solving soot population balance equation. Well established models are introduced in these equations for the chemistry of PAH in ethylene combustion, for particle nucleation, growth, agglomeration and oxidation. These closures are combined with a stochastic approach, which drives the evolution of a fixed number of computational particles used to solve for the particle size distribution with a control of agglomeration and numerical roundoff error through a fixed sectional discretisation. A laminar sooting flame is simulated to compare the results against measurements and previous numerical simulations, confirming the validity of the novel approach in terms of accuracy and CPU efficiency. The relation between the mobility diameter, measured in the experiments, and the equivalent sphere diameter, introduced in the modeling, is discussed under this novel numerical framework. The influence of the fractal particle shape on the simulated particle size distribution is explored. Finally, Particle Size Distributions obtained from the hybrid method are compared to the ones obtained with a representative fixed-sectional method.

中文翻译：

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层流预混火焰中烟尘粒度分布的分析：混合随机/固定截面方法

通过求解总数量密度的平衡方程和颗粒尺寸的概率密度函数，解决了火焰中烟尘粒径分布的数值模拟，从而得到了求解烟尘种群平衡方程的混合随机/固定截面方法。在这些方程中引入了完善的模型，用于分析乙烯燃烧中 PAH 的化学性质、粒子成核、生长、团聚和氧化。这些闭包与随机方法相结合，该方法驱动固定数量的计算粒子的演变，用于通过固定截面离散化控制聚集和数值舍入误差来求解粒度分布。模拟层流烟尘火焰，将结果与测量值和先前的数值模拟进行比较，证实了新方法在准确性和 CPU 效率方面的有效性。在这个新颖的数值框架下讨论了实验中测量的迁移率直径与建模中引入的等效球体直径之间的关系。探讨了分形颗粒形状对模拟粒度分布的影响。最后，将从混合方法获得的粒度分布与使用代表性固定截面方法获得的粒度分布进行比较。在建模中引入，在这个新颖的数值框架下进行了讨论。探讨了分形颗粒形状对模拟粒度分布的影响。最后，将从混合方法获得的粒度分布与使用代表性固定截面方法获得的粒度分布进行比较。在建模中引入，在这个新颖的数值框架下进行了讨论。探讨了分形颗粒形状对模拟粒度分布的影响。最后，将从混合方法获得的粒度分布与使用代表性固定截面方法获得的粒度分布进行比较。