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物理化学学报  2019, Vol. 35 Issue (2): 167-181    DOI: 10.3866/PKU.WHXB201803022
论文     
典型燃料点火延迟时间的一阶和二阶局部和全局敏感度分析
席双惠1,王繁1,*(),李象远2
1 四川大学原子与分子物理研究所,成都 610065
2 四川大学化学工程学院,成都 610065
First- and Second-Order Local and Global Sensitivity Analyses on Ignition Delay Times of Four Typical Fuels
Shuanghui XI1,Fan WANG1,*(),Xiangyuan LI2
1 Institute of Atomic and Molecular Physics, Sichuan University, Chengdu 610065, P. R. China
2 College of Chemical Engineering, Sichuan University, Chengdu 610065, P. R. China
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摘要:

本文中,我们计算氢气和一些典型的碳氢化合物燃料的化学动力学机理中,点火延迟时间相对于反应速率常数的一阶和二阶全局和局部敏感系数。在敏感度分析中,模型的输出选为点火延迟时间的自然对数,而输入参数是反应速率常数所乘比例因子的自然对数。在本文的敏感度分析中,模型的输出表示为最多同时依赖于两个输入参数的多项式函数。通过改变一个或者两个输入参数来确定这个多项式函数,而局部敏感度系数和全局敏感度系数通过这个多项式很容易得到。与基于高维模型表示法(HDMR)的全局敏感度分析相比,这种方法需要相对少量的样本。我们的结果显示,全局敏感度分析所确定的重要反应与局部敏感度分析的结果非常类似,这是因为输入参数只在较小范围内变化。某些情况下,一个重要反应与一个次要反应可能具有相对较大的二阶敏感度系数。本文所发展的敏感度分析方法提供了燃烧机理中对燃烧特性影响显著的反应信息,以及两个反应相互耦合对燃烧特性的影响。此外,它还可以用来辅助RS-HDMR进行全局敏感度分析,进而更加可靠地确定全局敏感度系数。

关键词: 全局敏感度分析局部敏感度分析点火延迟时间化学燃烧机理    
Abstract:

Sensitivity analysis is an important tool in model validation and evaluation that has been employed extensively in the analysis of chemical kinetic models of combustion processes. The input parameters of a chemical kinetic model are always associated with some uncertainties, and the effects of these uncertainties on the predicted combustion properties can be determined through sensitivity analysis. In this work, first- and second-order global and local sensitivity coefficients of ignition delay time with respect to the scaling factor for reaction rate constants in chemical kinetic mechanisms for combustion of H2, methane, n-butane, and n-heptane are examined. In the sensitivity analysis performed here, the output of the model is taken to be natural logarithm of ignition delay time and the input parameters are the natural logarithms of the factors that scale the reaction rate constants. The output of the model is expressed as a polynomial function of the input parameters, with up to coupling between two input parameters in the present sensitivity analysis. This polynomial function is determined by varying one or two input parameters, and allows the determination of both local and global sensitivity coefficients. The order of the polynomial function in the present work is four, and the factor that scales the reaction rate constant is in the range from 1/e to e, where e is the base of the natural logarithm. A relatively small number of sample runs are required in this approach compared to the global sensitivity analysis based on the highly dimensional model representation method, which utilizes random sampling of input (RS-HDMR). In RS-HDMR, sensitivity coefficients are determined only for the rate constants of a limited number of reactions; the present approach, by contrast, affords sensitivity coefficients for a larger number of reactions. Reactions and reaction pairs with the largest sensitivity coefficients are listed for ignition delay times of four typical fuels. Global sensitivity coefficients are always positive, while local sensitivity coefficients can be either positive or negative. A negative local sensitivity coefficient indicates that the reaction promotes ignition, while a positive local sensitivity coefficient suggests that the reaction actually suppresses ignition. Our results show that important reactions or reaction pairs identified by global sensitivity analysis are usually rather similar to those based on local sensitivity analysis. This finding can probably be attributed to the fact that the values of input parameters are within a rather small range in the sensitivity analysis, and nonlinear effects for such a small range of parameters are negligible. It is possible to determine global sensitivity coefficients by varying the input parameters over a larger range using the present approach. Such analysis shows that correlation effects between an important reaction and a minor reaction can have relatively sizable second-order sensitivity coefficient in some cases. On the other hand, first-order global sensitivity coefficients in the present approach will be affected by coupling between two reactions, and some results of the first-order global sensitivity analysis will be different from those determined by local sensitivity analysis or global sensitivity analysis under conditions where the correlation effects of two reactions are neglected. The present sensitivity analysis approach provides valuable information on important reactions as well as correlated effects of two reactions on the combustion characteristics of a chemical kinetic mechanism. In addition, the analysis can also be employed to aid global sensitivity analysis using RS-HDMR, where global sensitivity coefficients are determined more reliably.

Key words: Global sensitivity analysis    Local sensitivity analysis    Ignition delay time    Chemical mechanism for combustion
收稿日期: 2017-12-18 出版日期: 2018-03-02
中图分类号:  O643  
基金资助: 国家重点研发计划(2017YFB0202400);国家重点研发计划(2017YFB0202401);国家自然科学基金(21473116);国家自然科学基金(21773160)
通讯作者: 王繁     E-mail: wangf44@gmail.com
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引用本文:

席双惠,王繁,李象远. 典型燃料点火延迟时间的一阶和二阶局部和全局敏感度分析[J]. 物理化学学报, 2019, 35(2): 167-181, 10.3866/PKU.WHXB201803022

Shuanghui XI,Fan WANG,Xiangyuan LI. First- and Second-Order Local and Global Sensitivity Analyses on Ignition Delay Times of Four Typical Fuels. Acta Phys. -Chim. Sin., 2019, 35(2): 167-181, 10.3866/PKU.WHXB201803022.

链接本文:

http://www.whxb.pku.edu.cn/CN/10.3866/PKU.WHXB201803022        http://www.whxb.pku.edu.cn/CN/Y2019/V35/I2/167

Fig 1  First-order global and local sensitivity coefficients of important reaction on ignition delay time of H2.
Fig 2  Second-order global and local sensitivity coefficients of important pairs of reactions on ignition delay time of H2.
Fig 3  First-order global and local sensitivity coefficients of important reaction on ignition delay time of CH4.
Fig 4  Second-order global and local sensitivity coefficients of important pairs of reactions on ignition delay time of CH4.
Fig 5  Ignition delay time versus scaling factor for rate constant of reaction No. 71 in reaction mechanism of methane at T = 1000 K and p = 20 Pa. In Fig 5a, rate constants of both the forward and the backward reactions are scaled, in Fig. 5b, only the forward reaction rate constant is scaled, in Fig 5c, only the backward reaction rate constant is scaled.
Fig 6  First-order global and local sensitivity coefficients of important reaction on ignition delay time of n-butane.
Fig 7  Second-order global and local sensitivity coefficients of important pairs of reactions on ignition delay time of n-butane.
Fig 8  First-order global and local sensitivity coefficients of important reaction on ignition delay time of n-heptane.
Fig 9  Second-order global and local sensitivity coefficients of important pairs of reactions on ignition delay time of n-heptane.
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