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Frontiers in Energy

Front. Energy    2019, Vol. 13 Issue (2) : 367-376
Applicability of high dimensional model representation correlations for ignition delay times of n-heptane/air mixtures
Wang LIU, Jiabo ZHANG, Zhen HUANG, Dong HAN()
Key Laboratory of Power Machinery and Engineering of the Ministry of Education, Shanghai Jiao Tong University, Shanghai 200240, China
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It is difficult to predict the ignition delay times for fuels with the two-stage ignition tendency because of the existence of the nonlinear negative temperature coefficient (NTC) phenomenon at low temperature regimes. In this paper, the random sampling-high dimensional model representation (RS-HDMR) methods were employed to predict the ignition delay times of n-heptane/air mixtures, which exhibits the NTC phenomenon, over a range of initial conditions. A detailed n-heptane chemical mechanism was used to calculate the fuel ignition delay times in the adiabatic constant-pressure system, and two HDMR correlations, the global correlation and the stepwise correlations, were then constructed. Besides, the ignition delay times predicted by both types of correlations were validated against those calculated using the detailed chemical mechanism. The results showed that both correlations had a satisfactory prediction accuracy in general for the ignition delay times of the n-heptane/air mixtures and the stepwise correlations exhibited a better performance than the global correlation in each subdomain. Therefore, it is concluded that HDMR correlations are capable of predicting the ignition delay times for fuels with two-stage ignition behaviors at low-to-intermediate temperature conditions.

Keywords ignition delay      random sampling      high dimensional model representation      n-heptane      fuel kinetics     
Corresponding Authors: Dong HAN   
Just Accepted Date: 27 July 2018   Online First Date: 10 September 2018    Issue Date: 04 July 2019
 Cite this article:   
Wang LIU,Jiabo ZHANG,Zhen HUANG, et al. Applicability of high dimensional model representation correlations for ignition delay times of n-heptane/air mixtures[J]. Front. Energy, 2019, 13(2): 367-376.
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Fig.1  ID times versus initial temperature for n-heptane/air mixtures under changed pressures and equivalence ratios
Fig.2  ID times versus initial pressure for n-heptane/air mixtures under changed temperatures and equivalence ratios
Fig.3  Comparison of the ID times predicted by using the global correlation (τHDMR) and calculated by using the detailed chemical mechanism (τCHEM)
Fig.4  ID times versus initial temperature for n-heptane/air mixtures at different initial conditions
Subdomains Temperature/K Pressure/atm
1 650≤T0 ≤900 5≤P ≤20
2 650≤T0 ≤900 20≤P ≤50
3 900≤T0 ≤1250 5≤P ≤20
4 900≤T0 ≤1250 20≤P ≤50
Tab.1  Initial temperature and pressure ranges for four subdomains
Subdomains R2(global correlation) R2(stepwise correlation)
1 0.9046 0.9726
2 0.8958 0.9526
3 0.9608 0.9802
4 0.9621 0.9687
Tab.2  Coefficients of determination for each subdomain
Fig.5  Comparison of the ID times predicted by using the stepwise correlations (τHDMR) and calculated by using the detailed chemical mechanism (τCHEM)
Fig.6  ID time trends versus pressure for n-heptane/air mixtures at different initial temperatures and equivalence ratios
Simulated ID times/log10τ(s) Global correlation (1)/log10τ(s) Relative error/% Measured ID times/log10τ(s) Global correlation (2)/log10τ(s) Relative error/%
–3.90 –3.77 3.33 –4.07 –3.7 9.09
–3.44 –3.28 4.65 –3.49 –3.60 –3.15
–3.08 –3.04 1.29 –3.08 –3.51 –13.96
–2.91 –2.93 –0.68 –2.94 –3.45 –16.66
–2.8 –2.84 –1.42 –3.00 –3.36 –12.00
–2.84 –2.78 2.11 –3.07 –3.25 –5.86
–2.82 –2.73 3.19 –3.03 –3.10 –2.27
–2.72 –2.65 2.57 –3.00 –2.96 0.99
–2.65 –2.60 1.88 –2.84 –2.91 –2.46
–2.37 –2.35 0.84 –2.51 –2.74 –9.16
–2.06 –2.00 2.91 –1.98 –2.59 –30.80
Tab.3  Prediction performances of global correlations (1) and (2) (680 K<T<1200 K, P = 41 atm, j = 0.5)
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