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Nonmodal stability in Hagen-Poiseuille flow of a shear thinning fluid
Liu R(刘荣); Liu QS(刘秋生); Liu, R; Chinese Acad Sci, Inst Mech, Natl Micrograv Lab, Key Lab Micrograv, Beijing 100190, Peoples R China.
Source PublicationPhysical Review E
2012-06-22
Volume85Issue:6Pages:066318
ISSN1539-3755
AbstractLinear stability in Hagen-Poiseuille flow of a shear-thinning fluid is considered. The non-Newtonian viscosity is described by the Carreau rheological law. The effects of shear thinning on the stability are investigated using the energy method and the nonmodal stability theory. The energy analysis shows that the nonaxisymmetric disturbance with the azimuthal wave number m = 1 has the lowest critical energy Reynolds number for both the Newtonian and shear-thinning cases. With the increase of shear thinning, the critical energy Reynolds number decreases for both the axisymmetric and nonaxisymmetric cases. For the nonmodal stability, we focus on two problems: response to external excitations and response to initial conditions. The former is studied by examining the epsilon pseudospectrum, and the latter by examining the energy growth function G(t). For both Newtonian and shear-thinning fluids, it is found that there can be a rather large transient growth even though the linear operator of the Hagen-Poiseuille flow has no unstable eigenvalue. For the problem of response to external excitations, the optimal response is achieved by disturbance with m = 1 for both the Newtonian and non-Newtonian cases. For the problem of response to initial conditions, the optimal disturbance is in the form of streamwise uniform streaks. Being different from the Newtonian case, the azimuthal wave number of the optimal disturbance may be greater than 1 for strongly shear-thinning cases.
KeywordPipe-flow Transition Turbulence Instability
Subject Area流动的稳定性
DOI10.1103/PhysRevE.85.066318
URL查看原文
Indexed BySCI ; EI
Language英语
WOS IDWOS:000305568200002
WOS KeywordPIPE-FLOW ; TRANSITION ; TURBULENCE ; INSTABILITY
WOS Research AreaPhysics
WOS SubjectPhysics, Fluids & Plasmas ; Physics, Mathematical
Funding OrganizationThis work was supported by National Natural Science Foundation of China (Grants No. 11102211, No. 50890182, and No. 11072249) and the Knowledge Innovation Program of Chinese Academy of Sciences (KGCX-SW-409).
DepartmentNML流动稳定性与复杂流动
Classification一类
Citation statistics
Document Type期刊论文
Identifierhttp://dspace.imech.ac.cn/handle/311007/46595
Collection国家微重力实验室
Corresponding AuthorLiu, R; Chinese Acad Sci, Inst Mech, Natl Micrograv Lab, Key Lab Micrograv, Beijing 100190, Peoples R China.
Recommended Citation
GB/T 7714
Liu R,Liu QS,Liu, R,et al. Nonmodal stability in Hagen-Poiseuille flow of a shear thinning fluid[J]. Physical Review E,2012,85(6):066318.
APA 刘荣,刘秋生,Liu, R,&Chinese Acad Sci, Inst Mech, Natl Micrograv Lab, Key Lab Micrograv, Beijing 100190, Peoples R China..(2012).Nonmodal stability in Hagen-Poiseuille flow of a shear thinning fluid.Physical Review E,85(6),066318.
MLA 刘荣,et al."Nonmodal stability in Hagen-Poiseuille flow of a shear thinning fluid".Physical Review E 85.6(2012):066318.
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