Open Access

ARTICLE

Linear Stability Analysis of Time-Averaged Flow Past a Cylinder

Sanjay Mittal¹

1 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.

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Keywords

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