Численное моделирование характеристик зажигания цилиндрического тепловыделяющего образца в среде со случайными колебаниями температуры
https://doi.org/10.26907/2541-7746.2024.3.343-363
Аннотация
Рассмотрена задача тепловой устойчивости цилиндрического образца с нелинейным тепловыделением при случайном блуждании температуры окружающей среды. Исследовано поведение такой системы в зависимости от параметров задачи (интенсивности тепловыделения, дисперсии случайного блуждания). Для этого предложен численный алгоритм, основанный на усреднении множества реализаций случайного блуждания внешней температуры. Разработан численный метод решения задачи теплопроводности с источником и со случайными условиями на границе, сочетающий явные и неявные схемы для линеаризованных уравнений переноса и метод Эйлера – Маруямы. Получены распределения характеристик зажигания и моменты этих распределений, установлена их зависимость от параметров задачи.
Ключевые слова
тепловой взрыв,
стохастическое дифференциальное уравнение,
математическое моделирование,
метод Монте-Карло
При поддержке: Исследование выполнено за счет гранта Российского научного фонда № 23-29-00406 (https://rscf.ru/project/23-29-00406/)
Об авторе
И. Г. Донской
Институт систем энергетики им. Л.А. Мелентьева СО РАН
Россия
Россия
Донской Игорь Геннадьевич - доктор технических наук, старший научный сотрудник.
Ул. Лермонтова, д. 130, Иркутск, 664033
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Рецензия
Для цитирования:
Донской И.Г. Численное моделирование характеристик зажигания цилиндрического тепловыделяющего образца в среде со случайными колебаниями температуры. Ученые записки Казанского университета. Серия Физико-математические науки. 2024;166(3):343-363. https://doi.org/10.26907/2541-7746.2024.3.343-363
For citation:
Donskoy I.G. Numerical Modeling of the Ignition Characteristics of a Cylindrical Heat-Generating Sample in a Medium with Stochastic Temperature Variations. Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki. 2024;166(3):343-363. (In Russ.) https://doi.org/10.26907/2541-7746.2024.3.343-363
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