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Two-dimensional compressible viscous flow around a circular cylinder

Published online by Cambridge University Press:  23 November 2015

Daniel Canuto  and
Kunihiko Taira
Daniel Canuto
Affiliation:
Department of Mechanical Engineering, Florida A&M/Florida State University, Tallahassee, FL 32310, USA
Kunihiko Taira*
Affiliation:
Department of Mechanical Engineering, Florida A&M/Florida State University, Tallahassee, FL 32310, USA
*
†Email address for correspondence: ktaira@fsu.edu
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Abstract

Direct numerical simulation is performed to study compressible viscous flow around a circular cylinder. The present study considers two-dimensional shock-free continuum flow by varying the Reynolds number between 20 and 100 and the free-stream Mach number between 0 and 0.5. The results indicate that compressibility effects elongate the near wake for cases above and below the critical Reynolds number for two-dimensional flow under shedding. The wake elongation becomes more pronounced as the Reynolds number approaches this critical value. Moreover, we determine the growth rate and frequency of linear instability for cases above the critical Reynolds number. From the analysis, it is observed that the frequency of the Bénard–von Kármán vortex street in the time-periodic fully saturated flow increases from the dominant unstable frequency found from the linear stability analysis as the Reynolds number increases from its critical value, even for the low range of Reynolds numbers considered. We also find that the compressibility effects reduce the growth rate and dominant frequency in the linear growth stage. Semi-empirical functional relationships for the growth rate and the dominant frequency in linearized flow around the cylinder in terms of the Reynolds number and free-stream Mach number are presented.

JFM classification

Compressible Flows: Compressible Flows Instability: Instability Wakes/Jets: Wakes
Type
Papers
Information
Journal of Fluid Mechanics , Volume 785 , 25 December 2015 , pp. 349 - 371
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Copyright
© 2015 Cambridge University Press 

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Footnotes

‡

Present address: Department of Mechanical and Aerospace Engineering, University of California, Los Angeles, CA 90095, USA.

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