CRITICAL CONDITIONS OF SELF-IGNITION AT BIFURCATION POINTS
- Authors: Philippov А.А.1, Berlin A.A.1
-
Affiliations:
- N.N. Semenov Federal Research Center for Chemical Physics, Russian Academy of Sciences
- Issue: Vol 510, No 1 (2023)
- Pages: 35-38
- Section: ФИЗИКА
- URL: https://journals.rcsi.science/2686-7400/article/view/135936
- DOI: https://doi.org/10.31857/S2686740023030069
- EDN: https://elibrary.ru/OYKPNT
- ID: 135936
Cite item
Abstract
The article summarizes the results of the main research in the field of self-ignition theory. For symmetrical vessels, the following are presented: critical conditions of spontaneous ignition in dimensional coordinates, temperature distribution in the vessel, pre-explosive heating of fuel and the critical size of the vessel at the time of explosion. It is noted that the self-ignition conditions for different vessels differ only by a digital multiplier, which indicates that the shape of the vessel does not affect the physic-chemical processes going on in the fuel at the time of the explosion. Each singular point, being a bifurcation point, determines a number that allows finding a single critical condition of self–ignition from the set of solutions to the heat equation. This condition, in the coordinates of its variables, represents a multidimensional surface separating the zone of stationary existence of a combustible system from the zone of “no return”, where a combustible system cannot exist.
About the authors
А. А. Philippov
N.N. Semenov Federal Research Center for Chemical Physics, Russian Academy of Sciences
Author for correspondence.
Email: 7987961@mail.ru
Russia, Moscow
A. A. Berlin
N.N. Semenov Federal Research Center for Chemical Physics, Russian Academy of Sciences
Email: 7987961@mail.ru
Russia, Moscow
References
- Франк-Каменецкий Д.А. Диффузия и теплопередача в химической кинетике. 2-е изд. пер. и доп. М.: Наука, 1967.
- Зельдович Я.Б., Баренблатт Г.И., Либрович В.Б., Махвиладзе Г.М. Математическая теория горения и взрыва. М.: Наука, 1980.
- Гельфанд И.М. Задачи теории квазилинейных уравнений // УМН. 1959. Т. 154. № 4, параграф 15 (Баренблатт Г.И.). С. 787–790.
- Фомичев А.В. Элементы теории бифуркации и динамических систем. М.: МФТИ, 2019. Ч. 1.
- Арнольд В.И. Теория катастроф. М.: Наука, 1990.
- Филиппов А.А., Берлин А.А. Математическая теория зажигания накаленной поверхностью // Доклады РАН. Физика, технические науки. 2022. Т. 503. С. 24–30.