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A novel method for chemistry tabulation of strained premixed/stratified flames based on principal component analysis

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Abstract

The principal component analysis (PCA) is used to analyze the high dimensional chemistry data of laminar premixed/stratified flames under strain effects. The first few principal components (PCs), which have larger contribution ratios, are chosen as the tabulated scalars to build the look-up chemistry table. Prior tests show that the strained premixed flame structure can be well reconstructed. To highlight the physical meanings of the tabulated scalars in the stratified flames, a modified PCA method is developed, where the mixture fraction is used to replace one of the PCs with the highest correlation coefficient with a mixture fraction. The other two tabulated scalars are then modified with the Schmidt orthogonalization. The modified tabulated scalars not only have clear physical meanings, but also contain passive scalars. The PCA method has good commonality, and can be extended for building the thermo-chemistry table including strain rate effects when different fuels are used.

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Abbreviations

φ :

equivalent ratio

a :

strain rate

yk :

kth species mass fraction vector

Y :

mass fraction matrix

F :

principal component (PC) matrix

U :

PC weight coefficient matrix

S :

covariance matrix

Λ :

characteristic root matrix

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Authors and Affiliations

  1. Department of Thermal Science and Energy Engineering, University of Science and Technology of China, Hefei, 230027, China

    Peng Tang, Taohong Ye, Zhou Yu & Zhaoyang Xia

  2. School of Mechatronics Engineering, Chizhou University, Chizhou, 247000, Anhui Province, China

    Peng Tang

  3. Shenyang Engine Research Institute, Aero Engine (Group) Corporation of China, Shenyang, 110015, China

    Hongda Zhang

Authors
  1. Peng Tang
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  2. Hongda Zhang
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  3. Taohong Ye
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  4. Zhou Yu
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  5. Zhaoyang Xia
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Correspondence to Taohong Ye.

Additional information

Citation: Tang, P., Zhang, H. D., Ye, T. H., Yu, Z., and Xia, Z. Y. A novel method for chemistry tabulation of strained premixed/stratified flames based on principal component analysis. Applied Mathematics and Mechanics (English Edition) (2018) https://doi.org/10.1007/s10483-018-2326-6

Project supported by the National Natural Science Foundation of China (Nos. 91441117 and 51576182) and the Natural Key Program of Chizhou University (No. 2016ZRZ007)

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Tang, P., Zhang, H., Ye, T. et al. A novel method for chemistry tabulation of strained premixed/stratified flames based on principal component analysis. Appl. Math. Mech.-Engl. Ed. 39, 855–866 (2018). https://doi.org/10.1007/s10483-018-2326-6

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  • DOI: https://doi.org/10.1007/s10483-018-2326-6

Keywords

Chinese Library Classification

2010 Mathematics Subject Classification

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