A Lagrangian criterion of unsteady flow separation for two-dimensional periodic flows

doi:10.1007/s10483-018-2350-8

Applied Mathematics and Mechanics (English Edition) ›› 2018, Vol. 39 ›› Issue (7): 1007-1018.doi: https://doi.org/10.1007/s10483-018-2350-8

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A Lagrangian criterion of unsteady flow separation for two-dimensional periodic flows

Shuaibin HAN¹, Shuhai ZHANG¹, Hanxin ZHANG²

1. State Key Laboratory of Aerodynamics, China Aerodynamics Research and Development Center, Mianyang 621000, Sichuan Province, China;
2. China Aerodynamics Research and Development Center, Mianyang 621000, Sichuan Province, China

Received:2017-11-21 Revised:2018-02-18 Online:2018-07-01 Published:2018-07-01
Contact: Shuhai ZHANG E-mail:shuhai_zhang@163.com
Supported by:
Project supported by the National Natural Science Foundation of China (Nos. 11372340 and 11732016)

Abstract

Abstract: The present paper proposes a Lagrangian criterion of unsteady flow separation for two-dimensional periodic flows based on the principle of weighted averaging zero skin-friction given by Haller (HALLER, G. Exact theory of unsteady separation for two-dimensional flows. Journal of Fluid Mechanics, 512, 257-311 (2004)). By analyzing the distribution of the finite-time Lyapunov exponent (FTLE) along the no-slip wall, it can be found that the periodic separation takes place at the point of the zero FTLE. This new criterion is verified with an analytical solution of the separation bubble and a numerical simulation of lid-driven cavity flows.

Key words: orthotropic rectangular plate, nonlinear bending, method of twovariable, method of mixing perturbation, uniformly valid asymptotic solutions, two-dimensional periodic flow, unsteady flow separation, Lagrangian criterion, finite-time Lyapunov exponent(FTLE)

2010 MSC Number:

76N20
76-04

Shuaibin HAN, Shuhai ZHANG, Hanxin ZHANG. A Lagrangian criterion of unsteady flow separation for two-dimensional periodic flows. Applied Mathematics and Mechanics (English Edition), 2018, 39(7): 1007-1018.

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References

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A Lagrangian criterion of unsteady flow separation for two-dimensional periodic flows

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