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A stochastic approach to calculate the particle size distribution function of soot particles in laminar premixed flames

机译：计算层状预混火焰中烟尘颗粒粒径分布函数的随机方法

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摘要

We introduce an efficient stochastic approach to solve the population balance equation that describes the formation and oxidation of soot particles in a laminar premixed flame. The approach is based on a stochastic particle system representing the ensemble of soot particles. The processes contributing to the formation and oxidation of soot particles are treated in a probabilistic manner. The stochastic algorithm, which makes use of an efficient majorant kernel and the method of fictitious jumps, resolves the entire soot particle distribution (PSDF) without introducing additional closure assumptions. A fuel-rich laminar premixed acetylene flame is computed using a detailed kinetic soot model. Solutions are obtained for both, the stochastic approach and the method of moments combined with a modified version of the Premix, CHEMKIN code. In this manner, the accuracy of the method of moments in a laminar premixed flame simulation is investigated. It is found that the accuracy for the first moment is excellent (5% error), and mean error for rest of the moments is within 25%. Also the effect of the oxidation of the smallest particles (burnout) has been quantified but was found not to be important in the flame investigated. The time evolution of computed size distributions and their integral properties are compared to experimental measurements and the agreement was found to be satisfactory. Finally, the efficiency of the stochastic method is studied.
机译：我们引入了一种有效的随机方法来求解人口平衡方程，该方程描述了层状预混火焰中烟尘颗粒的形成和氧化。该方法基于代表烟灰颗粒集合的随机颗粒系统。以概率方式处理有助于烟灰颗粒形成和氧化的过程。随机算法利用有效的主要核和虚拟跳跃方法，可解决整个烟灰颗粒分布（PSDF），而无需引入其他封闭假设。使用详细的动力学煤烟模型来计算富含燃料的层流预混乙炔火焰。同时获得了随机方法和矩量方法以及预混合的修改版本CHEMKIN代码的解决方案。以这种方式，研究了层流预混火焰模拟中矩量法的准确性。发现第一时刻的精度极好（5％的误差），其余时刻的平均误差在25％以内。还已经量化了最小颗粒氧化（燃尽）的影响，但发现在研究的火焰中并不重要。将计算得到的尺寸分布及其整体性质的时间演变与实验测量结果进行比较，发现一致性令人满意。最后，研究了随机方法的效率。

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