The uncertainty in soot kinetics parameters will lead to uncertainty in the prediction of soot characteristics, including particle size distribution (PSD) and soot volume fraction (SVF). Uncertainty quantification is an important way to evaluate the model performance not only in terms of nominal accuracy but also in terms of confidence intervals. In this work, an uncertainty analysis approach combined with sensitivity analysis and the active subspace method is proposed. This approach is demonstrated with a sectional soot kinetics scheme for two laminar benchmark flames: the burner stabilized stagnation (BSS) flame with ethylene as the fuel, and the laminar diffusion flame on the Yale burner with methane as the fuel. The uncertainties of PSDs are obtained from an ensemble of kinetics samples and compared with the local sensitivities, while the uncertainties of SVFs are quantitatively evaluated via the active subspace and the response surface techniques. With an assumed soot kinetics uncertainty factor of , the uncertainties of soot volume fractions in the BSS flame at different heights are around . The peak soot volume fraction (PSVF) and peak soot volume fraction on the centerline (PSVF-c) in the Yale flame lie in the respective ranges of [0.91, 1.41] ppm and [0.84, 1.08] ppm for the 95% confidence intervals. Furthermore, the sensitivity of each reaction at different soot formation stages is quantitatively analyzed as a function of a newly defined soot progress variable. As expected, at the early stage of soot formation, SVFs are controlled by the nucleation reactions, especially reaction Rx3 (see Table1), and surface reactions gradually gain importance during the later stages of soot evolution. Ultimately, as indicated by the results of the Yale flame, the sensitivity of the surface growth reactions weakens, and oxidation and fragmentation reactions instead take control of the evolution of soot particles. These quantitative uncertainty results are performed for the first time and help reveal the control mechanism of soot formation in the studied flames.

中文翻译：

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截面法模拟层流火焰中烟灰形成的不确定度分析

烟尘动力学参数的不确定性将导致烟尘特性预测的不确定性，包括颗粒尺寸分布（PSD）和烟尘体积分数（SVF）。不确定性量化是评估模型性能的重要方法，不仅在名义精度方面，而且在置信区间方面。在这项工作中，提出了一种结合敏感性分析和活动子空间方法的不确定性分析方法。该方法通过两个层流基准火焰的截面烟灰动力学方案进行了演示：以乙烯为燃料的燃烧器稳定停滞（BSS）火焰，以及以甲烷为燃料的耶鲁燃烧器上的层流扩散火焰。 PSD 的不确定性是从动力学样本集合中获得的，并与局部灵敏度进行比较，而 SVF 的不确定性是通过活动子空间和响应面技术定量评估的。假设烟灰动力学不确定因子为 ，则不同高度 BSS 火焰中烟灰体积分数的不确定性约为 。对于 95% 置信区间，耶鲁火焰中的峰值烟灰体积分数 (PSVF) 和中心线上的峰值烟灰体积分数 (PSVF-c) 分别位于 [0.91, 1.41] ppm 和 [0.84, 1.08] ppm 范围内。此外，不同烟灰形成阶段的每个反应的敏感性作为新定义的烟灰进展变量的函数进行定量分析。正如预期的那样，在烟灰形成的早期阶段，SVF 受到成核反应的控制，特别是反应 Rx3（见表 1），并且在烟灰演化的后期阶段，表面反应逐渐变得重要。最终，正如耶鲁火焰的结果表明，表面生长反应的敏感性减弱，氧化和碎裂反应反而控制了烟灰颗粒的演变。这些定量的不确定性结果是首次进行，有助于揭示所研究的火焰中烟灰形成的控制机制。