Abstract

An approach to mathematically model the nucleation and growth of soot particles during the diffusion combustion of hydrocarbon fuel is presented. The chain of transformations of hydrocarbon fuel is modeled using a Markov process with a finite number of states, which is described by a stiff system of Kolmogorov’s ordinary differential equations (ODEs). As a result of numerical modeling, the set of functions describing the change in concentrations of various soot fractions in a laminar diffusion flame of toluene depending on time is obtained. Based on the results of the numerical solution of the ODE system, discrete particle size distributions (relative diameters) are constructed for different times. Continuous Weibull distributions approximating discrete distributions are constructed using the least squares method. The results obtained are in qualitative agreement with the experimental data.

中文翻译：

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甲苯扩散燃烧下烟灰形成的数学模型

摘要

提出了一种在碳氢化合物燃料扩散燃烧过程中对烟灰颗粒的成核和生长进行数学建模的方法。碳氢化合物燃料的转化链是使用具有有限状态数的马尔可夫过程进行建模的，该过程由Kolmogorov的常微分方程（ODE）的刚性系统描述。作为数值建模的结果，获得了描述时间的一组函数，该函数描述了甲苯层流扩散火焰中各种烟ot馏分浓度的变化。根据ODE系统的数值解结果，可以构建不同时间的离散粒度分布（相对直径）。使用最小二乘法构造近似离散分布的连续威布尔分布。