{"title":"多孔介质中自然对流对热点火的影响。2集总热模型1","authors":"V. Balakotaiah, P. Pourtalet","doi":"10.1098/rspa.1990.0073","DOIUrl":null,"url":null,"abstract":"In this paper, we examine the disappearance of criticality, ignition locus and bifurcation diagrams of temperature against Rayleigh number of a one-dimensional diffusion-convection-reaction model with the assumption of infinite thermal conductivity and zero species diffusivity. The predictions of this model are compared with those of the Semenov model to determine the impact of the species diffusion term. It is shown that for large values of the Rayleigh number (R* ≫ 1), the ignition locus may be expressed in a parametric form B Ls = t/ln t + t/(t - 1) (1 < t ≼ 3.4955), ψ/R* = (B Ls)2 ((t - 1)/t) exp{ - B Ls + B Ls/t} ln t, where B is the heat of reaction parameter, ψ is the Semenov number and Ls is a (modified) Lewis number. Criticality is found to disappear at B Ls = 4.194. When these results are compared with those of the Semenov model, it is found that neglecting the species diffusion term gives conservative approximations to the ignition locus, and criticality boundary. It is found that the lumped thermal model-I has five different types of bifurcation diagrams of temperature against Rayleigh number (single-valued, isola, inverse S, mushroom, inverse S + isola). These diagrams are qualitatively identical to the bifurcation diagrams of temperature against flow rate for the forced convection problem under the assumption of infinite thermal conductivity and zero species diffusivity.","PeriodicalId":20605,"journal":{"name":"Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"1990-06-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":"{\"title\":\"Natural convection effects on thermal ignition in a porous medium. II. Lumped thermal model-I\",\"authors\":\"V. Balakotaiah, P. Pourtalet\",\"doi\":\"10.1098/rspa.1990.0073\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper, we examine the disappearance of criticality, ignition locus and bifurcation diagrams of temperature against Rayleigh number of a one-dimensional diffusion-convection-reaction model with the assumption of infinite thermal conductivity and zero species diffusivity. The predictions of this model are compared with those of the Semenov model to determine the impact of the species diffusion term. It is shown that for large values of the Rayleigh number (R* ≫ 1), the ignition locus may be expressed in a parametric form B Ls = t/ln t + t/(t - 1) (1 < t ≼ 3.4955), ψ/R* = (B Ls)2 ((t - 1)/t) exp{ - B Ls + B Ls/t} ln t, where B is the heat of reaction parameter, ψ is the Semenov number and Ls is a (modified) Lewis number. Criticality is found to disappear at B Ls = 4.194. When these results are compared with those of the Semenov model, it is found that neglecting the species diffusion term gives conservative approximations to the ignition locus, and criticality boundary. It is found that the lumped thermal model-I has five different types of bifurcation diagrams of temperature against Rayleigh number (single-valued, isola, inverse S, mushroom, inverse S + isola). These diagrams are qualitatively identical to the bifurcation diagrams of temperature against flow rate for the forced convection problem under the assumption of infinite thermal conductivity and zero species diffusivity.\",\"PeriodicalId\":20605,\"journal\":{\"name\":\"Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1990-06-08\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"3\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1098/rspa.1990.0073\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1098/rspa.1990.0073","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 3
摘要
本文研究了在无限大导热系数和零扩散系数假设下一维扩散-对流-反应模型的临界、着火轨迹和温度分岔图随瑞利数的消失。将该模型的预测结果与Semenov模型的预测结果进行了比较,以确定物种扩散项的影响。结果表明,当瑞利数(R* > 1)较大时,引燃轨迹可以用参数形式表示:B Ls = t/ llnt + t/(t - 1) (1 < t - smitr3.4955), ψ/R* = (B Ls)2 ((t - 1)/t) exp{- B Ls + B Ls/t} llnt,其中B为反应热参数,ψ为Semenov数,Ls为(修正)路易斯数。发现临界性在bls = 4.194时消失。将这些结果与Semenov模型的结果进行比较,发现忽略物种扩散项可以得到点火轨迹和临界边界的保守逼近。发现集总热模型- 1具有5种不同类型的温度与瑞利数的分岔图(单值、孤立、逆S、蘑菇、逆S +孤立)。这些图与在无限大热导率和零种扩散率假设下强迫对流问题的温度对流量的分岔图在性质上是相同的。
Natural convection effects on thermal ignition in a porous medium. II. Lumped thermal model-I
In this paper, we examine the disappearance of criticality, ignition locus and bifurcation diagrams of temperature against Rayleigh number of a one-dimensional diffusion-convection-reaction model with the assumption of infinite thermal conductivity and zero species diffusivity. The predictions of this model are compared with those of the Semenov model to determine the impact of the species diffusion term. It is shown that for large values of the Rayleigh number (R* ≫ 1), the ignition locus may be expressed in a parametric form B Ls = t/ln t + t/(t - 1) (1 < t ≼ 3.4955), ψ/R* = (B Ls)2 ((t - 1)/t) exp{ - B Ls + B Ls/t} ln t, where B is the heat of reaction parameter, ψ is the Semenov number and Ls is a (modified) Lewis number. Criticality is found to disappear at B Ls = 4.194. When these results are compared with those of the Semenov model, it is found that neglecting the species diffusion term gives conservative approximations to the ignition locus, and criticality boundary. It is found that the lumped thermal model-I has five different types of bifurcation diagrams of temperature against Rayleigh number (single-valued, isola, inverse S, mushroom, inverse S + isola). These diagrams are qualitatively identical to the bifurcation diagrams of temperature against flow rate for the forced convection problem under the assumption of infinite thermal conductivity and zero species diffusivity.