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Asymptotic analysis of initial flow around an impulsively started circular cylinder using a Brinkman penalization method

Published online by Cambridge University Press:  27 October 2021

Y. Ueda Open the ORCID record for Y. Ueda [Opens in a new window]  and
T. Kida
Y. Ueda*
Affiliation:
Department of Mechanical Engineering, Faculty of Science and Engineering, Setsunan University, 17–8 Ikeda-Nakamachi, Neyagawa, Osaka572-8508, Japan
T. Kida
Affiliation:
Professor Emeritus, Osaka Prefecture University, 1-1 Gakuen-cho, Naka-ku, Sakai, Osaka,599-8531Japan
*
†Email address for correspondence: yoshiaki.ueda@mec.setsunan.ac.jp
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Abstract

The initial flow past an impulsively started translating circular cylinder is asymptotically analysed using a Brinkman penalization method on the Navier–Stokes equations. The asymptotic solution obtained shows that the tangential and normal slip velocities on the cylinder surface are of the order of $1/\sqrt {\lambda }$ and $1/\lambda$, respectively, within the second approximation of the present asymptotic analysis, where $\lambda$ is the penalization parameter. This result agrees with the estimation of Carbou & Fabrie (Adv. Diff. Equ., vol. 8, 2003, pp. 1453–1480). Based on the asymptotic solution, the influence of the penalization parameter $\lambda$ is discussed on the drag coefficient that is calculated using the adopted three formulae. It can then be found that the drag coefficient calculated from the integration of the penalization term exhibits a half-value of the results of Bar-Lev & Yang (J. Fluid Mech., vol. 72, 1975, pp. 625–647) as $\lambda \to \infty$.

JFM classification

Vortex Flows: Vortex dynamics Mathematical Foundations: Computational methods
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 929 , 25 December 2021 , A31
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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