Please wait a minute...
Acta Phys. -Chim. Sin.  2019, Vol. 35 Issue (2): 167-181    DOI: 10.3866/PKU.WHXB201803022
ARTICLE     
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
Download: HTML     PDF(4075KB) Export: BibTeX | EndNote (RIS)      

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 wordsGlobal sensitivity analysis      Local sensitivity analysis      Ignition delay time      Chemical mechanism for combustion     
Received: 18 December 2017      Published: 02 March 2018
MSC2000:  O643  
Fund:  the National Key R & D Program of China(2017YFB0202400);the National Key R & D Program of China(2017YFB0202401);the National Natural Science Foundation of China(21473116);the National Natural Science Foundation of China(21773160)
Corresponding Authors: Fan WANG     E-mail: wangf44@gmail.com
Cite this article:

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.

URL:

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

 
 
 
 
 
 
 
 
 
1 Tomlin A. S. ; Turányi T. Cleaner Combust. Green Energy Technol. 2013, 411.
2 Turányi, T. ; Tomlin, A. S. Analysis of Kinetic Reaction Mechanisms; Springer-Verlag: Berlin Heidelberg, German; 2014.
3 Tomlin A. S. Proc. Combust. Inst. 2013, 34, 159.
4 Saltelli A. ; Ratto M. ; Tarantola S. ; Campolongo F. Chem. Rev. 2005, 105, 2811.
5 Zádor J. ; Zsély I. G. ; Turányi T. Reliab. Eng. Syst. Saf. 2006, 91, 1232.
6 Wang H. ; Sheen D. A. Prog. Energy Combust. Sci. 2015, 47, 1.
7 Skodje R.T. ; Tomlin A. S. ; Klippenstein S. J. ; Harding L. B. ; Davis M. J. J. Phys. Chem. A 2010, 114, 8286.
8 Saltelli, A. ; Tarantola, S. ; Campolongo, F. ; Ratto, M. Sensitivity Analysis in Practice: A Guide to Assessing Scientific Models; John Wiley & Sons Ltd. : Chichester, UK; 2004.
9 Saltelli A. ; Ratto M. ; Tarantola S. ; Campolongo F. ; Commission E. Relia. Eng. Syst. Saf. 2006, 91 (10-11), 1109.
10 Saltelli, A. ; Ratto, M. ; Andres T. ; Campolongo, F. ; Cariboni, J. ; Gatelli, D. ; Sasana, M. ; Tarantola, S. Global Sensitivity Analisis: The Primer; John Wiley & Sons: Hoboken, NJ, USA; 2008.
11 Najm H. N. Annu. Rev. Fluid Mech. 2009, 41, 35.
12 Sobol I. M. Modelirovanie 1990, 2, 112.
13 Zsély I. G. ; Zádor J. ; Turányi T. Reliab. Eng. Syst. Saf. 1997, 57, 41.
14 Turányi, T. ; Rabitz, H. ; Saltelli, A. ; Chan, K. ; Scott, E. M. Sensitivity Analysis; Wiley: Chichester, UK; 2000.
15 McKay M. D. Reliab. Eng. Syst. Saf. 1997, 57, 267.
16 Xing L. ; Li S. ; Wang Z. ; Yang B. ; Klippenstein S. J. ; Zhang F. Combust. Flame 2015, 162, 3427.
17 Zheng X. L. ; Lu T. F. ; Law C. K. Proc. Combust. Inst. 2007, 31, 367.
18 Sankaran R. ; Hawkes E. R. ; Chen J. H. ; Lu T. F. ; Law C. K. Proc. Combust. Inst. 2007, 31, 1291.
19 Luo Z. ; Plomer M. ; Lu T. F. ; Som S. ; Longman D. E. ; Sarathy S. M. ; Pitz W. J. Fuel 2012, 99, 143.
20 Lu T. F. ; Law C. K. Combust. Flame 2008, 154, 153.
21 Niemeyer K. E. ; Sung C. J. Combust. Flame 2014, 161, 2752.
22 Niemeyer K. E. ; Sung C. J. ; Raju M. P. Combust. Flame 2010, 157, 1760.
23 Li R. ; Li S. H. ; Wang F. ; Li X. Y. Combust. Flame 2016, 166, 55.
24 SENKIN: A Fortran Program for Predicting Homogeneous Gas Phase Chemical Kinetics with Sensitivity Analysis. Available online: https://www.osti.gov/biblio/5371815 (accessed on February 28, 2018).
25 Turányi T. Tools Appl. J. Math. Chem. 1990, 5, 203.
26 Ziehn T. ; Tomlin A. S. Env. Model. Soft. 2009, 24, 775.
27 Sobol I. M. Math. Comp. Sim. 2001, 55, 271.
28 Li S. ; Yang B. ; Qi F. Combust. Flame 2016, 168, 53.
29 Ziehn T. ; Hughes K. J. ; Griffiths J. F. ; Porter R. ; Tomlin A. S. Combust. Theory Modell. 2009, 13, 589.
30 Tomlin A. S. ; Ziehn T. Lect. Notes Comput. Sci. Eng. 2010, 75, 9.
31 Saltelli A. ; Annoni P. ; Azzini I. ; Campolongo F. ; Ratto M. ; Tarantola S. Comput. Phys. Commun. 2010, 181, 259.
32 Davis M. J. ; Liu W. ; Sivaramakrishnan R. J. Phys.Chem.A 2017, 121 (3), 553.
33 Davis M. J. ; Skodje R. T. ; Tomlin A. S. J. Phys. Chem. A 2011, 115, 1556.
34 Ziehn T. ; Tomlin A. S. Int. J. Chem. Kinet. 2008, 40, 742.
35 Ziehn T. ; Tomlin A. S. Atmos. Environ. 2008, 42, 1857.
36 Zhou D. Y. ; Davis M. J. ; Skodje R. T. J. Phys. Chem. A 2013, 117, 3569.
37 Rabitz H. ; Alis ?. F. J. Math. Chem. 1999, 25, 197.
38 Wang S. W. ; Georgopoulos P. G. ; Li G. ; Rabitz H. Lect. Notes Comput. Sci. 2001, 2179, 326.
39 Brell G. ; Li G. ; Rabitz H. J. Chem. Phys. 2010, 132, 174103.
40 Alis ?. F. ; Rabitz H. J. Math. Chem. 2001, 29, 127.
41 Li G. ; Wang S. W. ; Rabitz H. J. Phys. Chem. A 2002, 106, 8721.
42 Li G. ; Wang S. W. ; Rabitz H. ; Wang S. ; Jaffé P. Chem. Eng. Sci. 2002, 57, 4445.
43 Feng X. J. ; Hooshangi S. ; Chen D. ; Li G. ; Weiss R. ; Rabitz H. Biophys. J. 2004, 87, 2195.
44 Rabitz H. ; Alis ?. F. ; Shorter J. ; Shim K. Comput. Phys. Commun. 1999, 117, 11.
45 Li G. ; Rabitz H. ; Wang S. W. ; Georgopoulos P. G. J. Comput. Chem. 2003, 24, 277.
46 Li G. ; Rabitz H. J. Comput. Chem. 2006, 27, 1112.
47 McKay M. D. Reliab. Eng. Syst. Saf. 1997, 57, 267.
48 O'Conaire M. ; Curran H. J. ; Simmie J. M. ; Pitz W. J. ; Westbrook C. K. Intl. J. Chem. Kinet. 2004, 36 (11), 603.
49 Konnov A. A. Combust. Flame 2008, 152, 507.
50 Wang Q. D. Acta Phys. -Chim. Sin 2016, 32, 595.
50 王全德. 物理化学学报, 2016, 32, 595.
51 Lu T. F. ; Law C. K. Combust. Inst. 2005, 30, 1333.
52 Li S. H. ; Li R. ; Guo J. J. ; Tan N. X. ; Wang F. ; Li X. Y. Acta Phys. -Chim. Sin. 2016, 32, 1623.
52 李树豪; 李瑞; 郭俊江; 谈宁馨; 王繁; 李象远. 物理化学学报, 2016, 32, 1623.
53 Jiang Y. ; Qiu R. Acta Phys. -Chim. Sin. 2009, 25, 1019.
53 蒋勇; 邱榕. 物理化学学报, 2009, 25, 1019.
54 Pepiot-Desjardins P. ; Pitsch H. Combust. Flame 2008, 154, 67.
55 Luo Z. ; Lu T. F. ; Maciaszek M. J. ; Som S. ; Longman D. E. Energy Fuels 2010, 24, 6283.
56 Sun W. ; Chen Z. ; Gou X. ; Ju Y. Combust. Flame 2010, 157, 1298.
57 Liu A. K. ; Jiao Y. ; Li S. H. ; Wang F. ; Li X. Y. Energy Fuels 2014, 28, 5426.
58 Available online: http://c3.nuigalway.ie/butane.html (accessed on February 28, 2018).
59 Mehl M. ; Pitz W. J. ; Westbrook C. K. ; Curran H. J. Proc. Combust. Inst. 2011, 33 (1), 193.
60 Mehl M. ; Pitz W. J. ; Sj?berg M. ; Dec J. E. SAE Tech. Paper. 2009, 1, 1806.
[1] Pengfei LU,Yudan GOU,Jiuning HE,Ping LI,Changhua ZHANG,Xiangyuan LI. Shock Tube Study of Methyl Pentanoate Ignition at High Temperatures[J]. Acta Phys. -Chim. Sin., 2018, 34(6): 618-624.
[2] Wei-Feng ZHANG,Lei-Yong XIAN,Kang-Le YONG,Jiu-Ning HE,Chang-Hua ZHANG,Ping LI,Xiang-Yuan LI. A Shock Tube Study of n-Undecane/Air Ignition Delays over a Wide Range of Temperatures[J]. Acta Phys. -Chim. Sin., 2016, 32(9): 2216-2222.
[3] ZHENG Zhao-Lei, LIANG Zhen-Long. Reduced Chemical Kinetic Model of a Gasoline Surrogate Fuel for HCCI Combustion[J]. Acta Phys. -Chim. Sin., 2015, 31(7): 1265-1274.
[4] HE Jiu-Ning, LI You-Liang, ZHANG Chang-Hua, LI Ping, LI Xiang-Yuan. Shock Tube Ignition Delay Measurements of Decalin/Air Mixtures at High Temperatures[J]. Acta Phys. -Chim. Sin., 2015, 31(5): 836-842.
[5] XU Jia-Qi, GUO Jun-Jiang, LIU Ai-Ke, WANG Jian-Li, TAN Ning-Xin, LI Xiang-Yuan. Construction of Autoignition Mechanisms for the Combustion of RP-3 Surrogate Fuel and Kinetics Simulation[J]. Acta Phys. -Chim. Sin., 2015, 31(4): 643-652.
[6] YAO Tong, ZHONG Bei-Jing. Chemical Kinetic Model for Auto-Ignition and Combustion of n-Decane[J]. Acta Phys. -Chim. Sin., 2013, 29(02): 237-244.
[7] ZHENG Dong, ZHONG Bei-Jing. Chemical Kinetic Model for Ignition of Three-Component Fuel Comprising iso-Octane/n-Heptane/Ethanol[J]. Acta Phys. -Chim. Sin., 2012, 28(09): 2029-2036.
[8] WEN Fei, ZHONG Bei-Jing. Skeletal Mechanism Generation Based on Eigenvalue Analysis Method[J]. Acta Phys. -Chim. Sin., 2012, 28(06): 1306-1312.
[9] TANG Hong-Chang, ZHANG Chang-Hua, LI Ping, WANG Li-Dong, YE Bin, LI Xiang-Yuan. Experimental Study of Autoignition Characteristics of Kerosene[J]. Acta Phys. -Chim. Sin., 2012, 28(04): 787-791.