ipolytechiPolytech JournaliPolytech Journal2782-40042782-6341Irkutsk National Research Technical University10.21285/1814-3520-2024-2-290-302HYUOIWipolytech-827Research ArticleЭНЕРГЕТИКАPOWER ENGINEERINGЗадача Стефана в тепловыделяющем цилиндрическом образце с граничными условиями третьего рода: расчёт времениStefan problem for a heat-generating cylindrical sample with boundary conditions of the third kind: calculation of melting timehttps://orcid.org/0000-0003-2309-8461ДонскойИ. Г.DonskoyI. G.

Донской Игорь Геннадьевич, к.т.н., старший научный сотрудник лаборатории термодинамики

664033, г. Иркутск, ул. Лермонтова, 130

Igor G. Donskoy, Cand. Sci. (Eng.), Senior Researcher of the Thermodynamics Laboratory

130 Lermontov St., Irkutsk 664033

donskoy.chem@mail.ruИнститут систем энергетики им. Л.А. Мелентьева СО РАНРоссияMelentiev Energy Systems Institute SB RASRussian Federation202404072024282290302Copyright © Донской И.Г., 20242024Донской И.Г.Donskoy I.G.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://ipolytech.elpub.ru/jour/article/view/827

Цель – установить кинетические закономерности расплавления тепловыделяющего цилиндрического элемента в заведомо надкритических условиях с помощью численного моделирования. Объектом исследования является процесс плавления в однородном образце, выделяющем теплоту за счет протекания реакции или электромагнитного нагрева. Теплофизические свойства образца принимаются постоянными в пределах твердой и жидкой фаз. Основным инструментом исследования является численная модель, построенная на основе нестационарной задачи Стефана в тепловыделяющем теле и включающая описание процессов теплопроводности и плавления. Фазовый переход описывается в энтальпийном представлении. Для выбора параметров численной модели (шагов сетки) проводится исследование точности разностной схемы. В результате проведенных исследований получены расчетные зависимости основных характеристик плавления (время расплавления и максимальная температура образца в момент расплавления) от управляющих параметров (интенсивность тепловыделения, величина теплового эффекта плавления, отношение коэффициентов теплопроводности фаз). С помощью некоторых приближений (усреднение температуры, квазистационарное распределение) получены формулы для оценки времени расплавления исследуемого образца. Расчеты показали, что изменение теплофизических свойств образца (коэффициентов теплопроводности, теплового эффекта) оказывает существенное влияние на скорость его плавления. Установлено, что зависимость времени расплавления от интенсивности тепловыделения и теплового эффекта фазового перехода качественно совпадает с приближенными моделями, но существенно отличается от них количественно, особенно в области малых отклонений от критической интенсивности тепловыделения.  Проведенные расчеты могут быть использованы при оценке термомеханической устойчивости материалов с внутренним тепловыделением. Разработанная численная модель дает возможность исследовать процессы плавления в широком диапазоне условий, в том числе при изменении граничных условий.

We determine the kinetic patterns of melting in a heat-generating cylindrical element under invariable supercritical conditions using numerical modelling. The study focuses on the melting process in a homogeneous sample that generates heat either through a chemical reaction or electromagnetic heating. The thermophysical properties of the sample were assumed to be constant in both solid and liquid phases. The main tool used in the study was a numerical model based on the nonstationary Stefan problem in a heat-generating body, which incorporates the descriptions of heat conduction and melting processes. The phase transition was described in terms of enthalpy. In order to select the parameters of the numerical model (grid steps), the accuracy of the difference scheme was investigated. The study presents calculated dependencies of the main melting characteristics (melting time and the maximum sample temperature at melting) on control parameters (heat generation intensity, the heat effect of melting and the ratio of thermal conductivity coefficients of the phases). By using specified approximations (temperature averaging and quasi-stationary distribution), formulas were derived to estimate the melting time of the sample. The calculations showed that the variations in the thermal properties of the sample (thermal conductivity coefficients and heat effect) significantly influence the melting rate. It was demonstrated that although the relationship between the melting time and the intensity of heat generation and the thermal effect of the phase transition is consistent with the approximate models, there is a significant quantitative difference between them, in particular, for small deviations from the critical heat generation intensity. The calculations can be used to assess the thermomechanical stability of materials with internal heat generation. The developed numerical model allows melting processes to be investigated under a wide range of conditions, including varying boundary conditions.

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The authors declare that there are no conflicts of interest present.