作旋转流动时非线性流体的改进模型

N·阿什拉菲; H·K·雷扎

doi:10.3879/j.issn.1000-0887.2012.11.007

作旋转流动时非线性流体的改进模型

doi: 10.3879/j.issn.1000-0887.2012.11.007

伊斯兰阿扎德大学科学研究部力学和航空航天工程学院,德黑兰,伊朗

详细信息

中图分类号: O357.1
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出版历程
- 收稿日期: 2011-04-13
- 修回日期: 2012-06-27
- 刊出日期: 2012-11-15

Improved Nonlinear Fluid Model in Rotating Flow

Department of Mechanical and Aerospace Engineering, Science and Research Branch,Islamic Azad University, Tehran, Iran

摘要

摘要: 在圆环结构中研究拟塑性流体作圆形的Couette流动．流体的粘度依赖于对守恒方程有直接影响的剪切率，守恒方程采用谱方法求解．可以证明所采用的拟塑性模型，可以被适当地表示为典型的非线性流动．在早期研究中，为了方便数值计算，粘度表达式中只考虑了剪切率的二次项，与此不同，这里考虑了二次幂项．圆形Couette流动中弯曲的流线，造成离心的不稳定性，引起环形的漩涡，称之为Taylor漩涡．进而发现，随着拟塑性影响的增加，临界Taylor数下降．与已有圆形Couette流动的实验相比较，两者有着良好的一致性．
- 拟塑性 /
- 圆形Couette流动 /
- 环形漩涡 /
- 谱方法
Abstract: Pseudoplastic circular Couette flow in annulus was investigated. The viscosity was dependent on the shear rate which directly affected the conservation equations that were solved by the spectral method in the present study. The pseudoplastic model adopted here proved suitable representative of nonlinear fluids. Unlike the previous studies where only the square of shear rate term in viscosity expression was considered to ease the numerical manipulations, in the present study the term containing the quadratic power was also taken into account. The curved streamlines of the circular Couette flow could cause a centrifugal instability leading to toroidal vortices, known as Taylor vortices. It is further found that the critical Taylor number becomes lower as the pseudoplastic effect increases. Comparison with existing measurements on pseudoplastic circular Couette flow results in good agreement.
- pseudoplastic /
- circular Couette flow /
- toroidal vortices /
- spectral method

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参考文献(22)

[1]	Taylor G I. Stability of a viscous liquid contained between two rotating cylinders[J]. Philos Trans R Soc London, Ser A, 1923, 223: 289-343.
[2]	Tagg R. The Couette-Taylor problem[J]. Nonlinear Science Today, 1994, 4: 2-25.
[3]	Gyr A, Bewersdorff H -W. Drag reduction of turbulent flows by additives[C]Fluid Mechanics and Its Applications, Vol 32. New York: Kluwer Academic, 1995.
[4]	Brenner M, Stone H. Modern classical physics through the work of G I Taylor[J]. Physics Today, 2000, 53(5): 30-35.
[5]	Hoffmann C, Altmeyer S, Pinter A, Lücke M. Transitions between Taylor vortices and spirals via wavy Taylor vortices and wavy spirals[J]. New J Physics, 2009, 11: 1-24. DOI 10.1088/1367-2630/11/5/053002.
[6]	Kuhlmann H. Model for Taylor-Couette flow[J]. Phys Rev A, 1985, 32(3): 1703-1707.
[7]	Berger H R. Mode analysis of Taylor-Couette flow in finite gaps[J]. Z Angew Math Mech, 1999, 79(2): 91-96. DOI 10.1002/(SICI)1521-4001(199902).
[8]	Li Z, Khayat R. A non-linear dynamical system approach to finite amplitude Taylor-Vortex flow of shear-thinning fluids[J]. Int J Numer Meth Fluids, 2004, 45(3): 321-340. DOI 10.1002/fld.703.
[9]	Ashrafi N. Stability analysis of shear-thinning flow between rotating cylinders[J]. Applied Mathematical Modelling, 2011, 35(9): 4407-4423. DOI 10.1016/j.apm.2011.03. 010.
[10]	Khayat R. Low-dimensional approach to nonlinear overstability of purely elastic Taylor-vortex flow[J]. Physical Review Letters, 1997, 78(26): 4918-4921.
[11]	Khayat R. Finite-amplitude Taylor-vortex flow of viscoelastic fluids[J]. Journal of Fluid Mechanics, 1999, 400: 33-58.
[12]	Muller S J, Shaqfeh E S G, Larson R G. Experimental study of the onset of oscillatory instability in viscoelastic Taylor-Couette flow[J]. Journal of Non-Newtonian Fluid Mechanics, 1993, 46: 315-330.
[13]	Larson R G. Instabilities in viscoelastic flows[J]. Rheol Acta, 1992, 31(3): 213-263.
[14]	Larson R G, Shaqfeh E S G, Muller S J. A purely elastic instability in Taylor-Couette flow[J]. Journal of Fluid Mechanics, 1990, 218: 573-600.
[15]	Dusting J, Balabani S. Mixing in a Taylor-Couette reactor in the non-wavy flow regime[J]. Chem Eng Sci, 2009, 64(13): 3103-3111.
[16]	Yorke J A, Yorke E D. Hydrodynamic Instabilities and the Transition to Turbulence[M]. Swinney H L, Gollub J P. Berlin: Springer-Verlag, 1981.
[17]	Yahata H. Temporal development of the Taylor vortices in a rotating field[J]. Prog Theor Phys, Supplement, 1978, 64: 176-185.
[18]	Bird R B, Armstrong R C, Hassager O. Dynamics of Polymeric Liquids[M]. 2nd ed. Vol 1. New York: Wiley, 1987.
[19]	Coronado-Matutti O, Souza Mendes P R, Carvalho M S. Instability of inelastic shear-thinning liquids in a Couette flow between concentric cylinders[J]. J Fluid Eng, 2004, 126(3): 385-390. DOI 10.1115/1.1760537.
[20]	Crumeryrolle O, Mutabazi I, Grisel M. Experimental study of inertioelastic Couette-Taylor instability modes in dilute and semidilute polymer solutions[J]. Physics of Fluids, 2002, 14(5): 1681-1688. DOI 10.1063/1.1466837.
[21]	Ashrafi N, Karimi Haghighi H. Effect of gap width on stability of non-Newtonian Taylor-Couette flow[J]. Z Angew Math Mech, 2012, 92(5): 393-408.
[22]	Strogatz S H. Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry and Engineering[M]. Rerseus Publishing, 1994.