Abstract
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.
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References
Huang Z, Li Z, Zhang J Y, et al. Active fuel design–a way to manage the right fuel for HCCI engines. Frontiers in Energy, 2016, 10(1): 14–28
Han D, Ickes A M, Bohac S V, et al. HC and CO emissions of premixed low-temperature combustion fueled by blends of diesel and gasoline. Fuel, 2012, 99(9): 13–19
Benajes J, Molina S, García A, et al. Performance and engine-out emissions evaluation of the double injection strategy applied to the gasoline partially premixed compression ignition spark assisted combustion concept. Applied Energy, 2014, 134(C): 90–101
Benajes J, García A, Domenech V, et al. An investigation of partially premixed compression ignition combustion using gasoline and spark assistance. Applied Thermal Engineering, 2013, 52(2): 468–477
Benajes J, Molina S, García A, et al. Effects of low reactivity fuel characteristics and blending ratio on low load RCCI (reactivity controlled compression ignition) performance and emissions in a heavy-duty diesel engine. Energy, 2015, 90: 1261–1271
Paykani A, Kakaee A H, Rahnama P, et al. Effects of diesel injection strategy on natural gas/diesel reactivity controlled compression ignition combustion. Energy, 2015, 90(1): 814–826
Yang Y, Dec J E, Sjöberg M, et al. Understanding fuel anti-knock performances in modern SI engines using fundamental HCCI experiments. Combustion and Flame, 2015, 162(10): 4008–4015
Han D, Lü X, Ma J J, et al. Influence of fuel supply timing and mixture preparation on the characteristics of stratified charge compression ignition combustion with n-heptane fuel. Combustion Science and Technology, 2009, 181(11): 1327–1344
Sadabadi K K, Shahbakhti M, Bharath A N, et al. Modeling of combustion phasing of a reactivity-controlled compression ignition engine for control applications. International Journal of Engine Research, 2016, 17(4): 421–435
Fatouraie M, Karwat DMA,WooldridgeMS. A numerical study of the effects of primary reference fuel chemical kinetics on ignition and heat release under homogeneous reciprocating engine conditions. Combustion and Flame, 2016, 163: 79–89
Kéromnès A, MetcalfeWK, Heufer K A, et al. An experimental and detailed chemical kinetic modeling study of hydrogen and syngas mixture oxidation at elevated pressures. Combustion and Flame, 2013, 160(6): 995–1011
Han D, Guang H, Yang Z, et al. Effects of equivalence ratio and carbon dioxide concentration on premixed charge compression ignition of gasoline and diesel-like fuel blends. Journal of Mechanical Science and Technology, 2013, 27(8): 2507–2512
Wang Y, Yang Z, Yang X, et al. Experimental and modeling studies on ignition delay times of methyl hexanoate/n-butanol blend fuels at elevated pressures. Energy & Fuels, 2014, 28(8): 5515–5522
Burke U, Somers K P, O’Toole P, et al. An ignition delay and kinetic modeling study of methane, dimethyl ether, and their mixtures at high pressures. Combustion and Flame, 2015, 162(2): 315–330
Kooshkbaghi M, Frouzakis C E, Boulouchos K. n-Heptane/air combustion in perfectly stirred reactors: dynamics, bifurcations and dominant reactions at critical conditions. Combustion and Flame, 2015, 162(9): 3166–3179
Burle S M, Metcalfe W, Herbinet O, et al. An experimental and modeling study of propene oxidation. Part 1: Speciation measurements in jet-stirred and flow reactors. Combustion and Flame, 2014, 161(11): 2765–2784
Sirjean B, Fournet R, Glaude P A, et al. A shock tube and chemical kinetic modeling study of the oxidation of 2,5-Dimethylfuran. Journal of Physical Chemistry A, 2013, 117(7): 1371–1392
Chen Z, Zhang P, Yang Y, et al. Impact of nitric oxide (NO) on n-heptane autoignition in a rapid compression machine. Combustion and Flame, 2017, 186: 94–104
Livengood J C, Wu P C. Correlation of autoignition phenomena in internal combustion engines and rapid compression machines. International Symposium on Combustion, 1955, 5(1): 347–356
Tao M, Han D, Zhao P. An alternative approach to accommodate detailed ignition chemistry in combustion simulation. Combustion and Flame, 2017, 176: 400–408
Donato N S, Petersen E L. Simplified correlation models for CO/H2 chemical reaction times. International Journal of Hydrogen Energy, 2008, 33(24): 7565–7579
Zhou A, Dong T, Akih-Kumgeh B. Simplifying ignition delay prediction for homogeneous charge compression ignition engine design and control. International Journal of Engine Research, 2016, 17(9): 957–968
Li G, Rosenthal C, Rabitz H. High dimensional model representations. Journal of Physical Chemistry A, 2001, 105(33): 7765–7777
Zhao Z, Chen Z, Chen S. Correlations for the ignition delay times of hydrogen/air mixtures. Chinese Science Bulletin, 2011, 56(2): 215–221
Zhao Z, Chen Z. HDMR correlations for the laminar burning velocity of premixed CH4/H2/O2/N2 mixtures. International Journal of Hydrogen Energy, 2012, 37(1): 691–697
Guang H, Yang Z, Huang Z, et al. Experimental study of n-heptane ignition delay with carbon dioxide addition in a rapid compression machine under low-temperature conditions. Chinese Science Bulletin, 2012, 57(30): 3953–3960
Li R, Liu Z, Han Y, et al. Experimental and kinetic modeling study of autoignition characteristics of n-heptane/ethanol by constant volume bomb and detail reaction mechanism. Energy & Fuels, 2017, 31(12): 13610–13626
Dagaut P, Reuillon M, Cathonnet M. Experimental study of the oxidation of n-heptane in a jet stirred reactor from low to high temperature and pressures up to 40 atm. Combustion and Flame, 1995, 101(1–2): 132–140
Shorter J A, Ip P C, Rabitz H A. An efficient chemical kinetics solver using high dimensional model representation. Journal of Physical Chemistry A, 1999, 103(36): 7192–7198
Li G, Rabitz H. Ratio control variate method for efficiently determining high-dimensional model representations. Journal of Computational Chemistry, 2006, 27(10): 1112–1118
Feng X J, Hooshangi S, Chen D, et al. Optimizing genetic circuits by global sensitivity analysis. Biophysical Journal, 2004, 87(4): 2195–2202
Ziehn T, Tomlin A S. Global sensitivity analysis of a 3D street canyon model-Part I: The development of high dimensional model representations. Atmospheric Environment, 2008, 42(8): 1857–1873
Li G, Wang S, Rabitz H. Practical approaches to construct RSHDMR component functions. Journal of Physical Chemistry A, 2002, 106(37): 8721–8733
Liu Y, Yousuff Hussaini M, Ökten G. Accurate construction of high dimensional model representation with applications to uncertainty quantification. Reliability Engineering & System Safety, 2016, 152: 281–295
Li G, Rabitz H, Wang S W, et al. Correlation method for variance reduction of Monte Carlo integration in RS-HDMR. Journal of Computational Chemistry, 2003, 24(3): 277–283
Li G, Hu J, Wang S W, et al. Random sampling-high dimensional model representation (RS-HDMR) and orthogonality of its different order component functions. Journal of Physical Chemistry A, 2006, 110(7): 2474–2485
Li G, Rabitz H, Hu J, et al. Regularized random-sampling high dimensional model representation (RS-HDMR). Journal of Mathematical Chemistry, 2008, 43(3): 1207–1232
Kee R J, Rupley F M, Miller J A. Sandia laboratories report 1989. Sandia National Laboratories, Albuquerque, NM, USA, 1989
Curran H J, Gaffuri P, Pitz W J, et al. A comprehensive modeling study of n-heptane oxidation. Combustion and Flame, 1998, 114(1–2): 149–177
Mehl M, Pitz W J, Westbrook C K, et al. Kinetic modeling of gasoline surrogate components and mixtures under engine conditions. Proceedings of the Combustion Institute, 2011, 33(1): 193–200
Mehl M, Pitz W, Sjöberg M, et al. Detailed kinetic modeling of low-temperature heat release for PRF fuels in an HCCI engine. SAE Technical Paper 2009–01–1806, 2009
Hall JM, RickardMJ A, Petersen E L. Comparison of characteristic time diagnostics for ignition and oxidation of fuel/oxidizer mixtures behind reflected shock waves. Combustion Science and Technology, 2005, 177(3): 455–483
Law C. Combustion Physics. Cambridge: Cambridge University Press, 2006
Zhang K, Banyon C, Bugler J, et al. An updated experimental and kinetic modeling study of n-heptane oxidation. Combustion and Flame, 2016, 172: 116–135
Ciezki H K, Adomeit G. Shock-tube investigation of selfignition of n-heptane-air mixtures under engine relevant conditions. Combustion and Flame, 1993, 93(4): 421–433
Heufer K A, Olivier H. Determination of ignition delay times of different hydrocarbons in a new high pressure shock tube. Shock Waves, 2010, 20(4): 307–316
Zeuch T, Moréac G, Ahmed S S, et al. A comprehensive skeletal mechanism for the oxidation of n-heptane generated by chemistry-guided reduction. Combustion and Flame, 2008, 155(4): 651–674
Peters N, Paczko G, Seiser R, et al. Temperature cross-over and nonthermal runaway at two-stage ignition of n-heptane. Combustion and Flame, 2002, 128(1–2): 38–49
Herzler J, Jerig L, Roth P. Shock tube study of the ignition of lean nheptane/air mixtures at intermediate temperatures and high pressures. Proceedings of the Combustion Institute, 2005, 30(1): 1147–1153
Maroteaux F, Noel L. Development of a reduced n-heptane oxidation mechanism for HCCI combustion modeling. Combustion and Flame, 2006, 146(1–2): 246–267
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This work was supported by the National Natural Science Foundation of China (Grant No. 51776124).
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Liu, W., Zhang, J., Huang, Z. et al. Applicability of high dimensional model representation correlations for ignition delay times of n-heptane/air mixtures. Front. Energy 13, 367–376 (2019). https://doi.org/10.1007/s11708-018-0584-9
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DOI: https://doi.org/10.1007/s11708-018-0584-9