{"title":"用椭球统计模型计算达西摩擦系数","authors":"O. V. Germider, V. N. Popov","doi":"10.1134/S0021894423040107","DOIUrl":null,"url":null,"abstract":"<p>This study describes a method for calculating the Darcy friction coefficient in a flat channel formed by two infinite parallel plates as a function of the Reynolds numbers and the gas rarefaction parameter in the channel. Maxwell’s diffuse reflection model is used as a model for the reflection of gas molecules from the channel walls. The isothermal gas flow is due to the presence of a pressure gradient that is small in absolute magnitude and directed along the channel walls. The method proposed in this paper is based on solving a linearized ellipsoidal-statistical Boltzmann kinetic equation with homogeneous boundary conditions using the Chebyshev polynomial approximation. An unknown function that interpolates the solution to this equation is represented as a partial sum of a series in Chebyshev polynomials of the first kind. The properties of finite sums for an orthonormal system of Chebyshev polynomials are used to reduce the problem to a system of linear algebraic equations with respect to the values of the sought function at interpolation nodes. The results obtained in this study are analyzed.</p>","PeriodicalId":608,"journal":{"name":"Journal of Applied Mechanics and Technical Physics","volume":null,"pages":null},"PeriodicalIF":0.5000,"publicationDate":"2023-10-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"DARCY FRICTION COEFFICIENT CALCULATED USING AN ELLIPSOIDAL STATISTICAL MODEL\",\"authors\":\"O. V. Germider, V. N. Popov\",\"doi\":\"10.1134/S0021894423040107\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>This study describes a method for calculating the Darcy friction coefficient in a flat channel formed by two infinite parallel plates as a function of the Reynolds numbers and the gas rarefaction parameter in the channel. Maxwell’s diffuse reflection model is used as a model for the reflection of gas molecules from the channel walls. The isothermal gas flow is due to the presence of a pressure gradient that is small in absolute magnitude and directed along the channel walls. The method proposed in this paper is based on solving a linearized ellipsoidal-statistical Boltzmann kinetic equation with homogeneous boundary conditions using the Chebyshev polynomial approximation. An unknown function that interpolates the solution to this equation is represented as a partial sum of a series in Chebyshev polynomials of the first kind. The properties of finite sums for an orthonormal system of Chebyshev polynomials are used to reduce the problem to a system of linear algebraic equations with respect to the values of the sought function at interpolation nodes. The results obtained in this study are analyzed.</p>\",\"PeriodicalId\":608,\"journal\":{\"name\":\"Journal of Applied Mechanics and Technical Physics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.5000,\"publicationDate\":\"2023-10-26\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Applied Mechanics and Technical Physics\",\"FirstCategoryId\":\"5\",\"ListUrlMain\":\"https://link.springer.com/article/10.1134/S0021894423040107\",\"RegionNum\":4,\"RegionCategory\":\"工程技术\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MECHANICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Applied Mechanics and Technical Physics","FirstCategoryId":"5","ListUrlMain":"https://link.springer.com/article/10.1134/S0021894423040107","RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MECHANICS","Score":null,"Total":0}
DARCY FRICTION COEFFICIENT CALCULATED USING AN ELLIPSOIDAL STATISTICAL MODEL
This study describes a method for calculating the Darcy friction coefficient in a flat channel formed by two infinite parallel plates as a function of the Reynolds numbers and the gas rarefaction parameter in the channel. Maxwell’s diffuse reflection model is used as a model for the reflection of gas molecules from the channel walls. The isothermal gas flow is due to the presence of a pressure gradient that is small in absolute magnitude and directed along the channel walls. The method proposed in this paper is based on solving a linearized ellipsoidal-statistical Boltzmann kinetic equation with homogeneous boundary conditions using the Chebyshev polynomial approximation. An unknown function that interpolates the solution to this equation is represented as a partial sum of a series in Chebyshev polynomials of the first kind. The properties of finite sums for an orthonormal system of Chebyshev polynomials are used to reduce the problem to a system of linear algebraic equations with respect to the values of the sought function at interpolation nodes. The results obtained in this study are analyzed.
期刊介绍:
Journal of Applied Mechanics and Technical Physics is a journal published in collaboration with the Siberian Branch of the Russian Academy of Sciences. The Journal presents papers on fluid mechanics and applied physics. Each issue contains valuable contributions on hypersonic flows; boundary layer theory; turbulence and hydrodynamic stability; free boundary flows; plasma physics; shock waves; explosives and detonation processes; combustion theory; multiphase flows; heat and mass transfer; composite materials and thermal properties of new materials, plasticity, creep, and failure.