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Theory of first-stage ignition delay in hydrocarbon NTC chemistry #34

Open syoukera opened 4 years ago

syoukera commented 4 years ago

@article{LIANG2018162, title = "Theory of first-stage ignition delay in hydrocarbon NTC chemistry", journal = "Combustion and Flame", volume = "188", pages = "162 - 169", year = "2018", issn = "0010-2180", doi = "https://doi.org/10.1016/j.combustflame.2017.10.003", url = "http://www.sciencedirect.com/science/article/pii/S0010218017303863", author = "Wenkai Liang and Chung K. Law", keywords = "Hydrocarbon, Low temperature chemistry, First-stage ignition, Ignition delay time", abstract = "The first-stage ignition delay of n-heptane/air mixtures is computationally studied using detailed mechanism and theoretically studied using eigenvalue analysis of simplified systems. Results show that the delay has a turnover behavior as temperature increases, being dominated by the competition of low-temperature branching and termination channels as well as the competition of forward and reverse reaction channels. As temperature increases to the intermediate range, the termination and reverse pathways result in a minimum in the delay, the state of which is theoretically derived. Simple analytical solutions for the delay as well as the species evolutions are presented to identify the rate constants that control the first-stage ignition and quantify the influence of the mixture composition, initial temperature and system pressure. It is further demonstrated that the above results also hold for n-octane/air and iso-octane/air mixtures." }

syoukera commented 4 years ago

Abstruct

syoukera commented 4 years ago

However

Recognizing that these previous theoretical predictions for the first-stage ignition delay [17], [18], [19] have mostly focused on the low-temperature segment of the first-ignition regime, within which the delay monotonically decreases with temperature, and as such have not been able to describe the local minimum behavior, the present study investigates the first-stage ignition delay from the low-temperature regime transitioning to the intermediate temperature regime, with due interest on the non-monotonic, local minimum behavior.

syoukera commented 4 years ago

Detailed simulation and reduced mechanism

image

syoukera commented 4 years ago

3. Eigenvalue analysis

image ここまでの式変形は追えた.行列の4行3列目にk_-4が不足しているのを見つけた

syoukera commented 4 years ago

Attachmentに使用した反応速度が記載されている.温度の関数になっている image

syoukera commented 4 years ago

ここからいきなり固有値が計算されてしまっているのだけれど,その方法はどうやっているのだろう?手計算か計算機を使用しているのか

syoukera commented 4 years ago

6×6の行列の固有値の求め方,よくわからん! 適当に調べたらScikit learnのPCAのドキュメントが出てきた https://scikit-learn.org/stable/modules/generated/sklearn.decomposition.PCA.html 計算機を使えば主成分分解(PCA)でできる?

syoukera commented 4 years ago

最大固有値と温度の関係 image

syoukera commented 4 years ago

最大固有値のモードへの各化学種の寄与 image

syoukera commented 4 years ago

初期条件(TPX)に対する依存性を考察するには固有値解析は良いみたいだけど,反応の途中で起こるトランジエントな変化を考察できない?組成と温度が変化するから? 今考えているのは,エネルギーの供給速度を変化させる[Oのプール]を発生させることだけど,境界条件として与えれば再現できる?横軸をOの濃度にして,縦軸に最大固有値を表示させる.