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Characteristics of the turbulent energy dissipation rate in a cylinder wake

Published online by Cambridge University Press:  27 November 2017

J. G. Chen Open the ORCID record for J. G. Chen [Opens in a new window] ,
Y. Zhou ,
R. A. Antonia  and
T. M. Zhou
J. G. Chen
Affiliation:
Institute for Turbulence-Noise-Vibration Interactions and Control, Harbin Institute of Technology (Shenzhen), Shenzhen 518055, China Digital Engineering Laboratory of Offshore Equipment, Shenzhen 518055, China School of Civil, Environmental and Mining Engineering, The University of Western Australia, 35 Stirling Highway, Crawley, WA 6009, Australia
Y. Zhou*
Affiliation:
Institute for Turbulence-Noise-Vibration Interactions and Control, Harbin Institute of Technology (Shenzhen), Shenzhen 518055, China Digital Engineering Laboratory of Offshore Equipment, Shenzhen 518055, China
R. A. Antonia
Affiliation:
School of Engineering, University of Newcastle, NSW 2308, Australia
T. M. Zhou
Affiliation:
School of Civil, Environmental and Mining Engineering, The University of Western Australia, 35 Stirling Highway, Crawley, WA 6009, Australia
*
†Email address for correspondence: [email protected]
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Abstract

This work aims to improve our understanding of the turbulent energy dissipation rate in the wake of a circular cylinder. Ten of the twelve velocity derivative terms which make up the energy dissipation rate are simultaneously obtained with a probe composed of four X-wires. Measurements are made in the plane of mean shear at $x/d=10$, 20 and 40, where $x$ is the streamwise distance from the cylinder axis and $d$ is the cylinder diameter, at a Reynolds number of $2.5\times 10^{3}$ based on $d$ and free-stream velocity. Both statistical and topological features of the velocity derivatives as well as the energy dissipation rate, approximated by a surrogate based on the assumption of homogeneity in the transverse plane, are examined. The spectra of the velocity derivatives indicate that local axisymmetry is first satisfied at higher wavenumbers while the departure at lower wavenumbers is caused by the Kármán vortex street. The spectral method proposed by Djenidi & Antonia (Exp. Fluids, vol. 53, 2012, pp. 1005–1013) based on the universality of the dissipation range of the longitudinal velocity spectrum normalized by the Kolmogorov scales also applies in the present flow despite the strong perturbation from the Kármán vortex street and violation of local isotropy at small $x/d$. The appropriateness of the spectral chart method is consistent with Antonia et al.’s (Phys. Fluids, vol. 26, 2014, 45105) observation that the two major assumptions in Kolmogorov’s first similarity hypothesis, i.e. very large Taylor microscale Reynolds number and local isotropy, can be significantly relaxed. The data also indicate that vorticity spectra are more sensitive, when testing the first similarity hypothesis, than velocity spectra. They also reveal that the velocity derivatives $\unicode[STIX]{x2202}u/\unicode[STIX]{x2202}y$ and $\unicode[STIX]{x2202}v/\unicode[STIX]{x2202}x$ play an important role in the interaction between large and small scales in the present flow. The phase-averaged data indicate that the energy dissipation is concentrated mostly within the coherent spanwise vortex rollers, in contrast with the model of Hussain (J. Fluid Mech., vol. 173, 1986, pp. 303–356) and Hussain & Hayakawa (J. Fluid Mech., vol. 180, 1987, p. 193), who conjectured that it resides mainly in regions of strong turbulent mixing.

JFM classification

Turbulent Flows: Turbulent Flows Wakes/Jets: Vortex streets Wakes/Jets: Wakes
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 835 , 25 January 2018 , pp. 271 - 300
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Copyright
© 2017 Cambridge University Press 

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