Existence regime of symmetric and asymmetric Taylor vortices in wide-gap spherical Couette flow
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作者:
Suhail Abbas
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机构:Chinese Academy of Sciences,LSEC and Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and Systems Science
Suhail Abbas
Li Yuan
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h-index: 0
机构:Chinese Academy of Sciences,LSEC and Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and Systems Science
Li Yuan
Abdullah Shah
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h-index: 0
机构:Chinese Academy of Sciences,LSEC and Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and Systems Science
Abdullah Shah
机构:
[1] Chinese Academy of Sciences,LSEC and Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and Systems Science
[2] School of Mathematical Sciences,Department of Mathematics
[3] University of Chinese Academy of Sciences,undefined
[4] COMSATS Institute of Information Technology,undefined
Spherical Couette flow;
Wide gap;
Symmetric Taylor vortices;
Asymmetric Taylor vortices;
D O I:
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中图分类号:
学科分类号:
摘要:
We study the existence regime of symmetric and asymmetric Taylor vortices in wide-gap spherical Couette flow by time marching the three-dimensional incompressible Navier–Stokes equations numerically. Three wide-gap clearance ratios, β=R2-R1/R1=0.33\documentclass[12pt]{minimal}
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\begin{document}$$\beta =\left( R_{2}-R_{1}\right) /R_{1}=0.33$$\end{document}, 0.38 and 0.42 are investigated for a range of Reynolds numbers respectively. Using the 1-vortex flow for clearance ratio β=0.18\documentclass[12pt]{minimal}
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\begin{document}$$\beta =0.18$$\end{document} at Reynolds number Re=700\documentclass[12pt]{minimal}
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\begin{document}$${Re}=700$$\end{document} as the initial conditions and suddenly increasing β\documentclass[12pt]{minimal}
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\begin{document}$$\beta$$\end{document} to the target value, we can compute Taylor vortices for the three wide gaps. For β=0.33\documentclass[12pt]{minimal}
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\begin{document}$$\beta =0.33$$\end{document}, Taylor vortices exist in the range 450≤Re≤2050\documentclass[12pt]{minimal}
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\begin{document}$$450\le {Re}\le 2050$$\end{document}. With increasing Re the steady symmetric 1-vortex flow becomes steady asymmetric at Re=1850\documentclass[12pt]{minimal}
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\begin{document}$${Re}=1850$$\end{document}, and then become periodic at Re=2000\documentclass[12pt]{minimal}
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\begin{document}$${Re}=2000$$\end{document}. When Re>2050\documentclass[12pt]{minimal}
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\begin{document}$${Re}>2050$$\end{document} the flow returns back to the steady basic flow state with no Taylor vortices. For β=0.38\documentclass[12pt]{minimal}
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\begin{document}$$\beta =0.38$$\end{document}, Taylor vortices can exist in the range 500≤Re≤1400\documentclass[12pt]{minimal}
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\begin{document}$$500\le {Re}\le 1400$$\end{document}. With increasing Re, the steady symmetric 1-vortex flow become steady asymmetric at Re=1200\documentclass[12pt]{minimal}
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\begin{document}$${Re}=1200$$\end{document}, and then the flow evolves into the steady basic flow for Re>1400\documentclass[12pt]{minimal}
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\begin{document}$${Re}>1400$$\end{document}. For β=0.42\documentclass[12pt]{minimal}
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\begin{document}$$\beta =0.42$$\end{document}, Taylor vortices can exist in the range 650≤Re≤1300\documentclass[12pt]{minimal}
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\begin{document}$$650\le {Re}\le 1300$$\end{document}. With increasing Re, steady asymmetric Taylor vortices occur at Re=1150\documentclass[12pt]{minimal}
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\begin{document}$${Re}=1150$$\end{document}, and then the flow evolves into the steady basic flow for Re>1300\documentclass[12pt]{minimal}
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\begin{document}$${Re}>1300$$\end{document}. The present numerical results are in good agreement with available numerical and experimental results. Furthermore, the existence regime of Taylor vortices in the (β,Re)\documentclass[12pt]{minimal}
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\begin{document}$$(\beta ,{Re})$$\end{document} plane for β≥0.33\documentclass[12pt]{minimal}
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\begin{document}$$\beta \ge 0.33$$\end{document} and the three-dimensional transition process from periodic asymmetric vortex flow to steady basic flow with increasing Re are presented for the first time.
机构:
Chinese Acad Sci, Acad Math & Syst Sci, LSEC, Beijing 100190, Peoples R China
Chinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math & Sci Engn Comp, Beijing 100190, Peoples R China
Univ Chinese Acad Sci, Sch Math Sci, Beijing 100190, Peoples R ChinaChinese Acad Sci, Acad Math & Syst Sci, LSEC, Beijing 100190, Peoples R China
Abbas, Suhail
Yuan, Li
论文数: 0引用数: 0
h-index: 0
机构:
Chinese Acad Sci, Acad Math & Syst Sci, LSEC, Beijing 100190, Peoples R China
Chinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math & Sci Engn Comp, Beijing 100190, Peoples R China
Univ Chinese Acad Sci, Sch Math Sci, Beijing 100190, Peoples R ChinaChinese Acad Sci, Acad Math & Syst Sci, LSEC, Beijing 100190, Peoples R China
Yuan, Li
Shah, Abdullah
论文数: 0引用数: 0
h-index: 0
机构:
COMSATS Inst Informat Technol, Dept Math, Islamabad, PakistanChinese Acad Sci, Acad Math & Syst Sci, LSEC, Beijing 100190, Peoples R China
机构:
Chinese Acad Sci, Acad Math & Syst Sci, LSEC, Beijing 100190, Peoples R China
Chinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math & Sci Engn Comp, Beijing 100190, Peoples R China
Univ Chinese Acad Sci, Sch Math Sci, Beijing 100190, Peoples R ChinaChinese Acad Sci, Acad Math & Syst Sci, LSEC, Beijing 100190, Peoples R China
Abbas, Suhail
Yuan, Li
论文数: 0引用数: 0
h-index: 0
机构:
Chinese Acad Sci, Acad Math & Syst Sci, LSEC, Beijing 100190, Peoples R China
Chinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math & Sci Engn Comp, Beijing 100190, Peoples R China
Univ Chinese Acad Sci, Sch Math Sci, Beijing 100190, Peoples R ChinaChinese Acad Sci, Acad Math & Syst Sci, LSEC, Beijing 100190, Peoples R China
Yuan, Li
Shah, Abdullah
论文数: 0引用数: 0
h-index: 0
机构:
COMSATS Inst Informat Technol, Dept Math, Islamabad, PakistanChinese Acad Sci, Acad Math & Syst Sci, LSEC, Beijing 100190, Peoples R China
机构:
Kansai Univ, Fac Engn Sci, Dept Pure & Appl Phys, Osaka 5648680, Japan
Osaka Univ, Grad Sch Engn Sci, Osaka 5608531, JapanKansai Univ, Fac Engn Sci, Dept Pure & Appl Phys, Osaka 5648680, Japan
Goto, Fumitoshi
Yoshikawa, Kazuki
论文数: 0引用数: 0
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机构:
Kansai Univ, Fac Engn Sci, Dept Pure & Appl Phys, Osaka 5648680, JapanKansai Univ, Fac Engn Sci, Dept Pure & Appl Phys, Osaka 5648680, Japan
Yoshikawa, Kazuki
Sugihara-Seki, Masako
论文数: 0引用数: 0
h-index: 0
机构:
Kansai Univ, Fac Engn Sci, Dept Pure & Appl Phys, Osaka 5648680, JapanKansai Univ, Fac Engn Sci, Dept Pure & Appl Phys, Osaka 5648680, Japan