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An entropy criterion for the validity of Navier-Stokes order continuum theory for gas-solid flow: Kinetic theory analysis
Zhao, Bidan1,2; Wang, Jing1,2; Wang, Junwu1
2017-11-23
Source PublicationCHEMICAL ENGINEERING SCIENCE
ISSN0009-2509
Volume172Issue:NOVPages:297-309
Abstract

Navier-Stokes order continuum theory (NS theory) established on the basis of local thermodynamic equilibrium (LTE) postulate has been widely used to study gas-solid flows. Qualitatively, the postulate is valid for systems sufficiently close to equilibrium, however, continuum theory provides no information on how small these deviations from equilibrium should be in order to guarantee the validity of LTE. To this end, kinetic theory analysis was carried out to formulate an entropy criterion, it was shown that (i) the entropy density up to the NS order is exactly the same as the one at the LTE condition, meaning that the LTE postulate is only valid for linear non-equilibrium regime, although NS theory and the LTE postulate are logically self-consistent; (ii) an entropy criterion characterizing the relative importance of nonlinear effects is derived, which should be small in order to make sure that the LTE postulate is valid and also sets the boundary of validity of NS theory; and (iii) the proposed entropy criterion, I-s << 1, is not only a function of granular temperature gradient and velocity gradient, but also a function of 1 - e(2) characterizing the inelasticity of particle-particle collisions. It is more complex and systematic than the traditional criterion based on the Knudsen number, Kn << 1. (C) 2017 Elsevier Ltd. All rights reserved.

KeywordEntropy Continuum Mechanics Gas-solid Flow Fluidization Kinetic Theory
SubtypeArticle
WOS HeadingsScience & Technology ; Technology
DOI10.1016/j.ces.2017.06.039
Indexed BySCI
Language英语
WOS KeywordRAPID GRANULAR FLOWS ; FLUIDIZED-BEDS ; 2-FLUID MODEL ; HYDRODYNAMIC EQUATIONS ; NUMERICAL-SIMULATION ; EULERIAN SIMULATION ; MOLECULAR CHAOS ; DRAG FORCE ; PARTICLES ; VELOCITY
WOS Research AreaEngineering
WOS SubjectEngineering, Chemical
Funding OrganizationNational Natural Science Foundation of China(21422608) ; Chinese Academy of Sciences(XDA07080200)
WOS IDWOS:000410833900025
Citation statistics
Cited Times:3[WOS]   [WOS Record]     [Related Records in WOS]
Document Type期刊论文
Identifierhttp://ir.ipe.ac.cn/handle/122111/23230
Collection多相复杂系统国家重点实验室
Affiliation1.Chinese Acad Sci, Inst Proc Engn, State Key Lab Multiphase Complex Syst, POB 353, Beijing 100190, Peoples R China
2.Univ Chinese Acad Sci, Beijing 100049, Peoples R China
Recommended Citation
GB/T 7714
Zhao, Bidan,Wang, Jing,Wang, Junwu. An entropy criterion for the validity of Navier-Stokes order continuum theory for gas-solid flow: Kinetic theory analysis[J]. CHEMICAL ENGINEERING SCIENCE,2017,172(NOV):297-309.
APA Zhao, Bidan,Wang, Jing,&Wang, Junwu.(2017).An entropy criterion for the validity of Navier-Stokes order continuum theory for gas-solid flow: Kinetic theory analysis.CHEMICAL ENGINEERING SCIENCE,172(NOV),297-309.
MLA Zhao, Bidan,et al."An entropy criterion for the validity of Navier-Stokes order continuum theory for gas-solid flow: Kinetic theory analysis".CHEMICAL ENGINEERING SCIENCE 172.NOV(2017):297-309.
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