A New-Type Counterpropagating Wave Pattern of Vertical Mirror Symmetry in Binary Fluid Convection

NING Li-zhong; QU Ya-wei; NING Bi-bo; YUAN Zhe; TIAN Wei-li; LIU Shuang

doi:10.21656/1000-0887.370367

Volume 38 Issue 11

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Article Navigation > Applied Mathematics and Mechanics > 2017 > 38(11): 1230-1239

NING Li-zhong, QU Ya-wei, NING Bi-bo, YUAN Zhe, TIAN Wei-li, LIU Shuang. A New-Type Counterpropagating Wave Pattern of Vertical Mirror Symmetry in Binary Fluid Convection[J]. Applied Mathematics and Mechanics, 2017, 38(11): 1230-1239. doi: 10.21656/1000-0887.370367

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A New-Type Counterpropagating Wave Pattern of Vertical Mirror Symmetry in Binary Fluid Convection

doi: 10.21656/1000-0887.370367

¹Institute of Water Resources and HydroElectric Engineering, Xi’an University of Technology, Xi’an 710048, P.R.China;²School of Architecture and Civil Engineering, Jiaxing University, Jiaxing, Zhejiang 314001, P.R.China;³China Water Resources Pearl River Planning Surveying & Designing Co. Ltd., Guangzhou 510610, P.R.China;⁴Department of Architecture, Shanghai University, Shanghai 200444, P.R.China

Funds: The National Natural Science Foundation of China(10872164)

Received Date: 2016-11-28
Rev Recd Date: 2017-05-14
Publish Date: 2017-11-15

Abstract

Abstract

The 2D hydrodynamic equations for binary fluid convection were numerically simulated with the SIMPLE method. For separation ratio ψ=－0.6 of the binary fluid mixture and aspect ratio Γ=20 of the rectangular cell, a newtype counterpropagating wave pattern of vertical mirror symmetry was found for the first time and its dynamics was preliminarily studied. At the center of the counterpropagating wave pattern of vertical mirror symmetry was a standing wave, of which the wavelength extended with time. As the wavelength increased to a certain critical value, a roll split into 2 rolls, and a new roll with a 180° phase difference formed between them 2. The roll located at the center line only has phase mutation and wavelength contraction or extension, without moving toward the left or right. The convective rolls propagating toward the left or right exist on both sides of the center line. The 2 phase mutations of the standing wave form a period, and the standing wave period increases with reduced Rayleigh number Ra_r. This type of convective structure exists in the range of Ra_r∈(3.6,4.3].The convection system produces the traveling wave pattern with defect for Ra_r≤3.6. The system shifts to the traveling wave pattern for Ra_r>4.3.The work shows that the counterpropagating wave pattern of vertical mirror symmetry is a stable flow pattern between the traveling wave pattern with defect and the traveling wave pattern.
- vertical mirror symmetry,
- counterpropagating wave pattern,
- standing wave,
- numerical simulation,
- binary fluid mixture

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References(35)

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