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Hydrodynamic damping of an oscillating cylinder at small Keulegan–Carpenter numbers

Published online by Cambridge University Press:  02 March 2021

Chengjiao Ren Open the ORCID record for Chengjiao Ren [Opens in a new window] ,
Lin Lu Open the ORCID record for Lin Lu [Opens in a new window] ,
Liang Cheng Open the ORCID record for Liang Cheng [Opens in a new window]  and
Tingguo Chen
Chengjiao Ren
Affiliation:
State Key Laboratory of Coastal and Offshore Engineering, Dalian University of Technology, Dalian116024, PR China Faculty of Infrastructure Engineering, Dalian University of Technology, Dalian116024, PR China
Lin Lu*
Affiliation:
State Key Laboratory of Coastal and Offshore Engineering, Dalian University of Technology, Dalian116024, PR China Faculty of Infrastructure Engineering, Dalian University of Technology, Dalian116024, PR China
Liang Cheng*
Affiliation:
State Key Laboratory of Coastal and Offshore Engineering, Dalian University of Technology, Dalian116024, PR China Faculty of Infrastructure Engineering, Dalian University of Technology, Dalian116024, PR China School of Engineering, The University of Western Australia, 35 Stirling Hwy, Crawley, WA6009, Australia
Tingguo Chen
Affiliation:
Faculty of Infrastructure Engineering, Dalian University of Technology, Dalian116024, PR China
*
†Email addresses for correspondence: lulin@dlut.edu.cn, liang.cheng@uwa.edu.au
†Email addresses for correspondence: lulin@dlut.edu.cn, liang.cheng@uwa.edu.au
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Abstract

Direct numerical simulations (DNS) of oscillatory flow around a cylinder show that the Stokes–Wang (S–W) solution agrees exceptionally well with DNS results over a much larger parameter space than the constraints of $\beta K^2\ll 1$ and $\beta \gg 1$ specified by the S–W solution, where $K$ is the Keulegan–Carpenter number and $\beta$ is the Stokes number. The ratio of drag coefficients predicted by DNS and the S–W solution, $\varLambda _K$, mapped out in the $K\text {--}\beta$ space, shows that $\varLambda _K < 1.05$ for $K\leq {\sim }0.8$ and $1 \leq \beta \leq 10^6$, which contradicts its counterpart based on experimental results. The large $\varLambda _K$ values are primarily induced by the flow separation on the cylinder surface, rather than the development of three-dimensional (Honji) instabilities. The difference between two-dimensional and three-dimensional DNS results is less than 2 % for $K$ smaller than the corresponding $K$ values on the iso-line of $\varLambda _K = 1.1$ with $\beta = 200\text {--}20\,950$. The flow separation actually occurs over the parameter space where $\varLambda _K\approx 1.0$. It is the spatio-temporal extent of flow separation rather than separation itself that causes large $\varLambda _K$ values. The proposed measure for the spatio-temporal extent, which is more sensitive to $K$ than $\beta$, correlates extremely well with $\varLambda _K$. The conventional Morison equation with a quadratic drag component is fundamentally incorrect at small $K$ where the drag component is linearly proportional to the incoming velocity with a phase difference of ${\rm \pi} /4$. A general form of the Morison equation is proposed by considering both viscous and form drag components and demonstrated to be superior to the conventional equation for $K < {\sim }2.0$.

JFM classification

Boundary Layers: Boundary layer separation Wakes/Jets: Separated flows
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 913 , 25 April 2021 , A36
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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