Uncertainty analysis of C-J detonation parameters based on polynomial chaos theory

LIANG Xiao; WANG Ruili; HU Xingzhi; CHEN Jiangtao

doi:10.11883/bzycj-2023-0030

Volume 43 Issue 10

Oct. 2023

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LIANG Xiao, WANG Ruili, HU Xingzhi, CHEN Jiangtao. Uncertainty analysis of C-J detonation parameters based on polynomial chaos theory[J]. Explosion And Shock Waves, 2023, 43(10): 104202. doi: 10.11883/bzycj-2023-0030

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LIANG Xiao, WANG Ruili, HU Xingzhi, CHEN Jiangtao. Uncertainty analysis of C-J detonation parameters based on polynomial chaos theory[J]. Explosion And Shock Waves, 2023, 43(10): 104202. doi: 10.11883/bzycj-2023-0030

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Uncertainty analysis of C-J detonation parameters based on polynomial chaos theory

doi: 10.11883/bzycj-2023-0030

1.
School of Mathematics and System Science, Shandong University of Science and Technology, Qingdao 266590, Shandong, China
2.
Beijing Institute of Applied Physics and Computational Mathematics, Beijing 100094, China
3.
China Aerodynamics Research and Development Center, Mianyang 6221000, Sichuan, China

Received Date: 2023-02-07
Accepted Date: 2023-07-04
Rev Recd Date: 2023-04-29
Publish Date: 2023-10-27

Abstract

Abstract

The Chapman-Jouguet theory is a powerful tool to predict the states of physical quantities at the rear of the shock front. However, uncertain factors and their influences on the system response quantities are neglected in the model of previous studies. Actually, the reliability and predictability of numerical simulation will be greatly affected by these uncertainties. To begin with, uncertainties of modeling and simulation of detonation process is discussed based on the detonation mechanism. Initial density and detonation velocity of PBX-9502 are assumed to satisfy the logarithmic normal distribution. The probability density functions (PDFs) of initial density and detonation velocity are derived from Anderson-Darling hypothesis test and parameter estimation combined with real experimental data. Beta distribution is utilized to cope with empirical parameters which have no physical meaning at all, with shaping parameters and supporting set are given according to the engineer’s experience. Rosenblatt transformation is used to transform the dependent and non-Gaussian random variables into independent standard Gaussian random variables. Furthermore, nonintrusive polynomial chaos (PC) method is used to study high dimensional uncertainty propagation of detonation waves. In particular, as for one variable PC, orthogonal polynomials are derived through Gram-Schmidt algorithm in Gauss-Hilbert space, Gauss integral formula with six quadrature points is used to compute coefficients of PC. Full tensor product of quadratures and weights is applied in PC of multivariate. PDF and corresponding Gaussian statistics such as expectation, standard deviation and confidence interval of quantity of interest (QoI) are obtained from the multivariate polynomial chaos. The result shows that the variation of detonation pressure is larger and the range of confidential interval is wider. It coincides with Professor Chengwei Sun’s conclusion that “The discreteness of detonation pressure is larger in experimental measurement”. The experimental data falls into the confidential interval of QoIs, then the reliability and robustness of the modeling is enhanced. And the methodology can be extended to the detonation system with much more complex equation of state.
- non-intrusive polynomial chaos,
- uncertainty quantification,
- Rosenblatt transformation,
- Anderson-Darling test,
- Chapman-Jouguet theory

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References(25)

References

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