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Low-Reynolds-number flow past a cylinder with uniform blowing or sucking

Published online by Cambridge University Press:  09 September 2015

C. A. Klettner  and
I. Eames
C. A. Klettner*
Affiliation:
Department of Mechanical Engineering, University College London, Torrington Place, London WC1E 7JE, UK
I. Eames
Affiliation:
Department of Mechanical Engineering, University College London, Torrington Place, London WC1E 7JE, UK
*
†Email address for correspondence: ucemkle@ucl.ac.uk
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Abstract

We analyse the low-Reynolds-number flow generated by a cylinder (of radius $a$) in a stream (of velocity $U_{\infty }$) which has a uniform through-surface blowing component (of velocity $U_{b}$). The flow is characterized in terms of the Reynolds number $Re$ ($=2aU_{\infty }/{\it\nu}$, where ${\it\nu}$ is the kinematic viscosity of the fluid) and the dimensionless blow velocity ${\it\Lambda}$ ($=U_{b}/U_{\infty }$). We seek the leading-order symmetric solution of the vorticity field which satisfies the near- and far-field boundary conditions. The drag coefficient is then determined from the vorticity field. For the no-blow case Lamb’s (Phil. Mag., vol. 21, 1911, pp. 112–121) expression is retrieved for $Re\rightarrow 0$. For the strong-sucking case, the asymptotic limit, $C_{D}\approx -2{\rm\pi}{\it\Lambda}$, is confirmed. The blowing solution is valid for ${\it\Lambda}<4/Re$, after which the flow is unsymmetrical about ${\it\theta}={\rm\pi}/2$. The analytical results are compared with full numerical solutions for the drag coefficient $C_{D}$ and the fraction of drag due to viscous stresses. The predictions show good agreement for $Re=0.1$ and ${\it\Lambda}=-5,0,5$.

JFM classification

Low-Reynolds-number flows: Low-Reynolds-number flows
Type
Rapids
Information
Journal of Fluid Mechanics , Volume 780 , 10 October 2015 , R2
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Copyright
© 2015 Cambridge University Press 

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