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The mode B structure of streamwise vortices in the wake of a two-dimensional blunt trailing edge

Published online by Cambridge University Press:  05 December 2019

Bradley Gibeau  and
Sina Ghaemi Open the ORCID record for Sina Ghaemi [Opens in a new window]
Bradley Gibeau
Affiliation:
Department of Mechanical Engineering, University of Alberta, Edmonton, AB T6G 2R3, Canada
Sina Ghaemi*
Affiliation:
Department of Mechanical Engineering, University of Alberta, Edmonton, AB T6G 2R3, Canada
*
†Email address for correspondence: [email protected]
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Abstract

The structure of streamwise vortices that arise due to secondary instabilities in the wake of a two-dimensional blunt body with a chord-to-thickness ratio of 12.5 was investigated using high-speed stereoscopic particle image velocimetry. Reynolds numbers spanning an order of magnitude from $Re(h)=2600$ to 25 800 were considered, where $h$ is the height of the blunt trailing edge. A modified two-dimensional $Q$-criterion ($Q^{\prime }=\unicode[STIX]{x1D714}_{x}Q/|\unicode[STIX]{x1D714}_{x}|$) was applied to identify the streamwise vortices. The wavelength of the streamwise vortices, defined as the spanwise distance between adjacent streamwise vortex pairs in the wake, was investigated by applying an autocorrelation algorithm to snapshots of $Q^{\prime }$. The most probable wavelength was found to range from $0.67h$ to $0.85h$ with increasing $Re$, and the mean wavelengths increased from $0.77h$ to $0.96h$. These wavelength values appeared to increase asymptotically. Visual inspection and cross-correlation analyses based on $Q^{\prime }$ showed that the streamwise vortices maintain their directions of rotation during primary shedding cycles. The latter analysis was carried out at low $Re$ because of a large amount of wake distortion and the absence of time-resolved data at high $Re$. The characteristics of the streamwise vortex structure found here match those of mode B, which, at similar $Re$, dominates the wakes of circular and square cylinders and has also recently been shown to exist in the wake of an elongated blunt body with a larger chord-to-thickness ratio of 46.5 (Gibeau et al., J. Fluid Mech., vol. 846, 2018, pp. 578–604).

JFM classification

Vortex Flows: Vortex shedding Wakes/Jets: Wakes
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 884 , 10 February 2020 , A12
Copyright
© 2019 Cambridge University Press

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