Nonmodal stability in Hagen-Poiseuille flow of a shear thinning fluid

	Nonmodal stability in Hagen-Poiseuille flow of a shear thinning fluid
	Liu R(刘荣); Liu QS(刘秋生); Liu, R
刊名	Physical Review E
	2012-06-22
通讯作者邮箱	liurong@imech.ac.cn;liu@imech.ac.cn
卷号	85 期号:6 页码:066318
关键词	Pipe-Flow Transition Turbulence Instability
ISSN号	1539-3755
通讯作者	Liu, R ; Chinese Acad Sci, Inst Mech, Natl Micrograv Lab, Key Lab Micrograv, Beijing 100190, Peoples R China.
产权排序	[Liu, Rong;Liu, Qiu Sheng] Chinese Acad Sci, Inst Mech, Natl Micrograv Lab, Key Lab Micrograv, Beijing 100190, Peoples R China
中文摘要	Linear 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.
学科主题	流动的稳定性
分类号	一类
类目[WOS]	Physics, Fluids & Plasmas ; Physics, Mathematical
研究领域[WOS]	Physics
关键词[WOS]	PIPE-FLOW ; TRANSITION ; TURBULENCE ; INSTABILITY
收录类别	SCI ; EI
资助信息	This 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).
原文出处	http://dx.doi.org/10.1103/PhysRevE.85.066318
语种	英语
WOS记录号	WOS:000305568200002
公开日期	2013-01-18
内容类型	期刊论文
源URL	[http://dspace.imech.ac.cn/handle/311007/46595]
专题	力学研究所_国家微重力实验室
通讯作者	Liu, R
推荐引用方式 GB/T 7714	Liu R,Liu QS,Liu, R. 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.(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.