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Flow instabilities in the wake of a rounded square cylinder

Published online by Cambridge University Press:  23 March 2016

Doohyun Park  and
Kyung-Soo Yang
Doohyun Park
Affiliation:
Department of Mechanical Engineering, Inha University, Incheon 22212, Republic of Korea
Kyung-Soo Yang*
Affiliation:
Department of Mechanical Engineering, Inha University, Incheon 22212, Republic of Korea
*
†Email address for correspondence: ksyang@inha.ac.kr
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Abstract

Instabilities in the flow past a rounded square cylinder have been numerically studied in order to clarify the effects of rounding the sharp edges of a square cylinder on the primary and secondary instabilities associated with the flow. Rounding the edges was done by inscribing a quarter circle of radius $r$ in each edge of a square cylinder of height $d$. Nine cases of rounding were considered, ranging from a square cylinder ($r/d=0$) to a circular cylinder ($r/d=0.5$) with an increment of 0.0625. Each cross-section was numerically implemented in a Cartesian grid system by using an immersed boundary method. The key parameters are the Reynolds number (Re) and the edge-radius ratio ($r/d$). For low Re, the flow is steady and symmetric with respect to the centreline. Over the first critical Reynolds number ($Re_{c1}$), the flow undergoes a Hopf bifurcation to a time-periodic flow, termed the primary instability. As Re further increases, the onset of the secondary instability of three-dimensional (3D) nature is detected beyond the second critical Reynolds number ($Re_{c2}$). Rounding the sharp edges of a square cylinder significantly affects the flow topology, leading to noticeable changes in both instabilities. By employing the Stuart–Landau equation, we investigated the criticality of the primary instability depending upon $r/d$. The onset of the 3D secondary instability was detected by using Floquet stability analysis. The temporal and spatial characteristics of the dominant modes (A, B, QP) were described. The neutral stability curves of each mode were computed depending upon $r/d$.

JFM classification

Instability: Instability Wakes/Jets: Separated flows Wakes/Jets: Wakes
Type
Papers
Information
Journal of Fluid Mechanics , Volume 793 , 25 April 2016 , pp. 915 - 932
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Copyright
© 2016 Cambridge University Press 

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