Multiple solutions and hysteresis in the flows driven by surface with antisymmetric velocity profile

doi:10.1088/1674-1056/abf7a6

中国物理B ›› 2021, Vol. 30 ›› Issue (9): 90201-090201.doi: 10.1088/1674-1056/abf7a6

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Multiple solutions and hysteresis in the flows driven by surface with antisymmetric velocity profile

Xiao-Feng Shi(石晓峰)¹, Dong-Jun Ma(马东军)^1,†, Zong-Qiang Ma(马宗强)¹, De-Jun Sun(孙德军)³, and Pei Wang(王裴)^1,2,†

1 Institute of Applied Physical and Computational Mathematics, Beijing 100094, China;
2 Center for Applied Physics and Technology, Peking University, Beijing 100871, China;
3 Department of Modern Mechanics, University of Science and Technology of China, Hefei 230027, China

收稿日期:2020-12-09 修回日期:2021-02-02 接受日期:2021-04-14 出版日期:2021-08-19 发布日期:2021-08-19
通讯作者: Dong-Jun Ma, Pei Wang E-mail:ma_dongjun@iapcm.ac.cn;wangpei@iapcm.ac.cn
基金资助:
Project supported by the National Natural Science Foundation of China (Grant Nos. 11902043 and 11772065), and the Science Challenge Project (Grant No. TZ2016001).

Multiple solutions and hysteresis in the flows driven by surface with antisymmetric velocity profile

Xiao-Feng Shi(石晓峰)¹, Dong-Jun Ma(马东军)^1,†, Zong-Qiang Ma(马宗强)¹, De-Jun Sun(孙德军)³, and Pei Wang(王裴)^1,2,†

1 Institute of Applied Physical and Computational Mathematics, Beijing 100094, China;
2 Center for Applied Physics and Technology, Peking University, Beijing 100871, China;
3 Department of Modern Mechanics, University of Science and Technology of China, Hefei 230027, China

Received:2020-12-09 Revised:2021-02-02 Accepted:2021-04-14 Online:2021-08-19 Published:2021-08-19
Contact: Dong-Jun Ma, Pei Wang E-mail:ma_dongjun@iapcm.ac.cn;wangpei@iapcm.ac.cn
Supported by:
Project supported by the National Natural Science Foundation of China (Grant Nos. 11902043 and 11772065), and the Science Challenge Project (Grant No. TZ2016001).

摘要/Abstract

摘要： Multiple steady solutions and hysteresis phenomenon in the square cavity flows driven by the surface with antisymmetric velocity profile are investigated by numerical simulation and bifurcation analysis. A high order spectral element method with the matrix-free pseudo-arclength technique is used for the steady-state solution and numerical continuation. The complex flow patterns beyond the symmetry-breaking at Re≈320 are presented by a bifurcation diagram for Re<2500. The results of stable symmetric and asymmetric solutions are consistent with those reported in literature, and a new unstable asymmetric branch is obtained besides the stable branches. A novel hysteresis phenomenon is observed in the range of 2208 < Re < 2262, where two pairs of stable and two pairs of unstable asymmetric steady solutions beyond the stable symmetric state coexist. The vortices near the sidewall appear when the Reynolds number increases, which correspond to the bifurcation of topology structure, but not the bifurcation of Navier-Stokes equations. The hysteresis is proposed to be the result of the combined mechanisms of the competition and coalescence of secondary vortices.

关键词: bifurcation and continuation, symmetry-breaking, hysteresis, surface driven cavity flow

Abstract: Multiple steady solutions and hysteresis phenomenon in the square cavity flows driven by the surface with antisymmetric velocity profile are investigated by numerical simulation and bifurcation analysis. A high order spectral element method with the matrix-free pseudo-arclength technique is used for the steady-state solution and numerical continuation. The complex flow patterns beyond the symmetry-breaking at Re≈320 are presented by a bifurcation diagram for Re<2500. The results of stable symmetric and asymmetric solutions are consistent with those reported in literature, and a new unstable asymmetric branch is obtained besides the stable branches. A novel hysteresis phenomenon is observed in the range of 2208 < Re < 2262, where two pairs of stable and two pairs of unstable asymmetric steady solutions beyond the stable symmetric state coexist. The vortices near the sidewall appear when the Reynolds number increases, which correspond to the bifurcation of topology structure, but not the bifurcation of Navier-Stokes equations. The hysteresis is proposed to be the result of the combined mechanisms of the competition and coalescence of secondary vortices.

Key words: bifurcation and continuation, symmetry-breaking, hysteresis, surface driven cavity flow

中图分类号: (Bifurcation theory)

02.30.Oz

47.20.Ky (Nonlinearity, bifurcation, and symmetry breaking) 47.15.Fe (Stability of laminar flows)

Xiao-Feng Shi(石晓峰), Dong-Jun Ma(马东军), Zong-Qiang Ma(马宗强), De-Jun Sun(孙德军), and Pei Wang(王裴). Multiple solutions and hysteresis in the flows driven by surface with antisymmetric velocity profile[J]. 中国物理B, 2021, 30(9): 90201-090201.

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Multiple solutions and hysteresis in the flows driven by surface with antisymmetric velocity profile

Multiple solutions and hysteresis in the flows driven by surface with antisymmetric velocity profile

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