Please wait a minute...
Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering)  0, Vol. 6 Issue (100): 1-7    DOI: 10.1631/jzus.2005.AS0001
Mechanical & Energy Engineering     
Non-axisymmetric instability in the Taylor-Couette flow of fiber suspension
WAN Zhan-hong, LIN Jian-zhong, YOU Zhen-jiang
Department of Mechanics, the State Key Laboratory of Fluid Power Transmission and Control, Zhejiang University, Hangzhou 310027, China; School of Informatics and Engineering, Flinders University of South Australia, GPO Box 2100, Adelaide, SA 5001, Australia
Download:   PDF(0KB)
Export: BibTeX | EndNote (RIS)      

Abstract  An analysis of the instability in the Taylor-Couette flow of fiber suspensions with respect to the non-axisymmetric disturbances was performed. The constitutive model proposed by Ericksen was used to represent the role of fiber additives on the stress tensor. The generalized eigenvalue equation governing the hydrodynamic stability of the system was solved using a direct numerical procedure. The results showed that the fiber additives can suppress the instability of the flow. At the same time, the non-axisymmetric disturbance is the preferred mode that makes the fiber suspensions unstable when the ratio of the angular velocity of the outer cylinder to that of the inner cylinder is a large negative number.

Key wordsFiber suspensions      Taylor-Couette flow      Hydrodynamic instability     
Received: 20 January 2005     
CLC:  O359  
Cite this article:

WAN Zhan-hong, LIN Jian-zhong, YOU Zhen-jiang. Non-axisymmetric instability in the Taylor-Couette flow of fiber suspension. Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering), 0, 6(100): 1-7.

URL:

http://www.zjujournals.com/xueshu/zjus-a/10.1631/jzus.2005.AS0001     OR     http://www.zjujournals.com/xueshu/zjus-a/Y0/V6/I100/1

[1]   Azaiez, J., 2000a. Linear stability of free shear flows of fiber suspensions. J. Fluid Mech., 404:179-209.
[2]   Azaiez, J., 2000b. Reduction of free shear flows instability: Effects of polymer versus fiber additives. J. Non-Newtonian Fluid Mech., 91:233-254.
[3]   Batchelor, G.K., 1971. The stress generated in a non-dilute suspension of elongational particles by pure straining. J. Fluid Mech., 46:813-829.
[4]   Blaise, N., 1994. Transition from circular Couette flow to Taylor vortex flow in dilute and semi-concentrated suspensions of stiff fibers. J. Phys. II France, 4:9-22.
[5]   Dinh, S.M., Armstrong, R.C., 1984. A rheological equation state for semi-concentrated fiber suspensions. J. Rheol., 28:207-227.
[6]   Erickson, J.L., 1960. Transversely isotropic fluids. Kolloid Z., 173:117-122.
[7]   Gupta, V.K., Sureshkumar, R., Khomami, B., Azaiez, J., 2002.
[8]   Centrifugal instability of semidilute non-Brownian fiber suspensions. J. Phys. Fluids, 14:1958-1971.
[9]   Hand, G.L., 1961. A theory of dilute suspensions. Arch. Rat. Mech. Anal., 7:81-86.
[10]   Hinch, E.J., Leal, L.G., 1972. The effect of Brownian motion on the rheological properties of a suspension of non-spherical particles. J. Fluid Mech., 52:683-712.
[11]   Frigaard, I., Nouar, C., 2003. On three-dimensional linear stability of Poiseuille flow of Bingham fluids. Phys. Fluids, 15:2843-2851.
[12]   Lin, J.Z., You, Z.J., 2003. Stability in the circular pipe flow of fiber suspensions. Journal of Hydrodynamics, 2:12-18.
[13]   Lin, J.Z., Zhang, L.X., 2003. On the structural features of fiber suspensions in converging channel flow. Journal of Zhejiang University SCIENCE, 4(4):400-406.
[14]   Orszag, S.A., 1971. An accurate solution of the Orr-Sommerfeld equation. J Fluid Mech., 50:689-703.
[15]   Pilipenko, V.N., Kalinichenko, N.M., Lemak, A.S., 1981. Stability of the flow of a fiber suspension in the gap between coaxial cylinders. Sov. Phys. Dokl., 26: 646-648.
[16]   Recktenwald, A., Lucke, M., Muller, H.W., 1993. Taylor vortex formation in axial through-flow: Linear and weakly nonlinear analysis. Phys. Rev. E, 48(6):4444-4454.
[17]   Shaqfeh, E.S.G., Frederickson, G.H., 1990. The hydrodynamic stress in a suspension of rods. Phys. Fluids, 2:7-24.
[18]   Trefethen, L.N., 2000. Spectral Methods in MATLAB. SIAM, Philadelphia, PA. Weideman, J.A.C., Reddy, S.C., 2000. A MATLAB differentiation matrix suite. ACM Transaction on Mathematical Software, 26(4):465-519.
[19]   You, Z.J., Lin, J.Z., Yu, Z.S., 2004. Hydrodynamic instability of fibre suspensions in channel flows. Fluid Dynamics Research, 34(4):251-271.
[1] Dong-fang Hu, Zheng-liang Huang, Jing-yuan Sun, Jing-dai Wang, Zu-wei Liao, Bin-bo Jiang, Jian Yang, Yong-rong Yang. Numerical simulation of gas-liquid flow through a 90° duct bend with a gradual contraction pipe[J]. Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering), 2017, 18(3): 212-224.
[2] Kai Zhang, Hong-bing Xiong, Xue-ming Shao. Dynamic modeling of micro- and nano-sized particles impinging on the substrate during suspension plasma spraying[J]. Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering), 2016, 17(9): 733-744.
[3] Hong-bing Xiong, Wen-guang Yu, Da-wei Chen, Xue-ming Shao. Numerical study on the aerodynamic performance and safe running of high-speed trains in sandstorms[J]. Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering), 2011, 12(12): 971-978.
[4] Xue-ming Shao, Jun Wan, Da-wei Chen, Hong-bing Xiong. Aerodynamic modeling and stability analysis of a high-speed train under strong rain and crosswind conditions[J]. Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering), 2011, 12(12): 964-970.
[5] Xiao-ke KU, Jian-zhong LIN. Motion and orientation of cylindrical and cubic particles in pipe flow with high concentration and high particle to pipe size ratio[J]. Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering), 2008, 9(5): 664-671.
[6] ZHOU Kun, LIN Jian-zhong. Research on 3D fiber orientation distribution in arbitrary planar flows[J]. Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering), 2007, 8(7): 1021-1025.
[7] XIE Ming-liang, LIN Jian-zhong, XING Fu-tang. On the hydrodynamic stability of a particle-laden flow in growing flat plate boundary layer[J]. Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering), 2007, 8(2): 17-.
[8] Govindarajan A. , Ramamurthy V. , Sundarammal K.. 3D couette flow of dusty fluid with transpiration cooling[J]. Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering), 2007, 8(2): 20-.
[9] CHANSON Hubert. Bubble entrainment, spray and splashing at hydraulic jumps[J]. Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering), 2006, 7(8): 1396-1405.
[10] CHEN Jie, GAO Dao-ming. Multi-objective genetic algorithm for the optimization of road surface cleaning process[J]. Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering), 2006, 7(8): 16-.
[11] Hu Ying-ying, Huang Zheng-ming. Coaxial liquid-liquid flows in tubes with limited length[J]. Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering), 2006, 7(3): 347-351.
[12] GAO Dao-ming, CHEN Jie, LU Jun-bo. Fuzzy prediction and experimental verification of road surface cleaning rate by pure waterjets[J]. Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering), 2005, 6(10): 18-.
[13] SHAO Xue-ming, LIN Jian-zhong, YU Zhao-sheng. Sedimentation of a single particle between two parallel walls[J]. Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering), 2004, 5(1): 111-116.
[14] LIN Jian-zhong, ZHANG Ling-xin. On the structural features of fiber suspensions in converging channel flow[J]. Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering), 2003, 4(4): 400-406.
[15] LIN Jian-zhong, ZHANG Wei-feng, WANG Ye-long. Research on the orientation distribution of fibers immersed in a pipe flow[J]. Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering), 2002, 3(5): 501-506.