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Linear Stability Analysis of Time-Averaged Flow Past a Cylinder

Sanjay Mittal1
Department of Aerospace Engineering, Indian Institute of Technology Kanpur, UP 208 016, India. Email: smit-tal@iitk.ac.in; Phone: +91 512 2597906; Fax: +91 5122597561.

Computer Modeling in Engineering & Sciences 2008, 27(1&2), 63-78. https://doi.org/10.3970/cmes.2008.027.063

Abstract

Flow past a circular cylinder looses stability at a Reynolds number,Re~47. It has been shown, in the past, that the linear stability analysis (LSA) of the steady state solution can predict not only the critical Re, but also the non-dimensional frequency, St, of the associated instability. For larger Re the non-linear effects become important and the LSA of the steady-state flow does not predict the correct St. It is shown that, in general, the LSA applied to the time-averaged flow can result in useful information regarding its stability. This idea is applied to the Re = 100 flow past a circular cylinder. The LSA of the time-averaged flow results in the correct value of St. Proper Orthogonal (POD) or Karhunen-Loéve (K-L) decomposition of the unsteady flow using the snapshot method is also carried out. The modes from this decomposition are compared to the unstable modes computed using the LSA.

Keywords

Circular Cylinder, Linear Stability Analysis, Finite Element Method, Reynolds Averaged Navier Stokes Equations, Proper Orthogonal Decomposition, Karhunen-Loéve (K-L) decomposition

Cite This Article

Mittal, S. (2008). Linear Stability Analysis of Time-Averaged Flow Past a Cylinder. CMES-Computer Modeling in Engineering & Sciences, 27(1&2), 63–78.



This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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