{"title":"Thermal Explosion of Single Particles in a Random Medium-Temperature Field","authors":"I. V. Derevich, A. K. Klochkov","doi":"10.1134/s0018151x23010030","DOIUrl":null,"url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>A model is proposed for the thermal explosion of a single particle with an exothermic chemical reaction in a turbulent temperature field of the medium. The chemical reaction rate is represented by a modified Arrhenius law, which takes into account changes in the internal structure of the particle material. Temperature fluctuations are modeled by a Gaussian random process. The study was carried out using the Lagrange and Euler approaches. In the Lagrange approach, in which a system of stochastic ordinary differential equations is solved, random temperature fluctuations of the medium and particle ensemble are calculated. Based on the results of numerical simulation of the ensemble, the dynamics of the empirical probability density function of the random particle temperature distribution is simulated. In the Euler approach, a nonstationary closed-loop equation is derived for the probability density function of random particle temperatures, which is numerically integrated using an original conservative difference scheme. The calculation results for both approaches agree satisfactorily with each other. It is shown that a random temperature field of the medium qualitatively changes the dynamics of occurrence of a thermal explosion. In a random temperature field, a thermal explosion can occur provided that in a deterministic case, the system is absolutely stable.</p>","PeriodicalId":13163,"journal":{"name":"High Temperature","volume":"9 1","pages":""},"PeriodicalIF":1.0000,"publicationDate":"2024-02-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"High Temperature","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.1134/s0018151x23010030","RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"PHYSICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
A model is proposed for the thermal explosion of a single particle with an exothermic chemical reaction in a turbulent temperature field of the medium. The chemical reaction rate is represented by a modified Arrhenius law, which takes into account changes in the internal structure of the particle material. Temperature fluctuations are modeled by a Gaussian random process. The study was carried out using the Lagrange and Euler approaches. In the Lagrange approach, in which a system of stochastic ordinary differential equations is solved, random temperature fluctuations of the medium and particle ensemble are calculated. Based on the results of numerical simulation of the ensemble, the dynamics of the empirical probability density function of the random particle temperature distribution is simulated. In the Euler approach, a nonstationary closed-loop equation is derived for the probability density function of random particle temperatures, which is numerically integrated using an original conservative difference scheme. The calculation results for both approaches agree satisfactorily with each other. It is shown that a random temperature field of the medium qualitatively changes the dynamics of occurrence of a thermal explosion. In a random temperature field, a thermal explosion can occur provided that in a deterministic case, the system is absolutely stable.
期刊介绍：
High Temperature is an international peer reviewed journal that publishes original papers and reviews written by theoretical and experimental researchers. The journal deals with properties and processes in low-temperature plasma; thermophysical properties of substances including pure materials, mixtures and alloys; the properties in the vicinity of the critical point, equations of state; phase equilibrium; heat and mass transfer phenomena, in particular, by forced and free convections; processes of boiling and condensation, radiation, and complex heat transfer; experimental methods and apparatuses; high-temperature facilities for power engineering applications, etc. The journal reflects the current trends in thermophysical research. It presents the results of present-day experimental and theoretical studies in the processes of complex heat transfer, thermal, gas dynamic processes, and processes of heat and mass transfer, as well as the latest advances in the theoretical description of the properties of high-temperature media.
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