Low-Reynolds-number flow past a cylinder with uniform blowing or sucking
CA Klettner, I Eames - Journal of Fluid Mechanics, 2015 - cambridge.org
Journal of Fluid Mechanics, 2015•cambridge.org
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 …
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 …
Abstract
We analyse the low-Reynolds-number flow generated by a cylinder (of radius ) in a stream (of velocity ) which has a uniform through-surface blowing component (of velocity ). The flow is characterized in terms of the Reynolds number (, where is the kinematic viscosity of the fluid) and the dimensionless blow velocity (). 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 . For the strong-sucking case, the asymptotic limit, , is confirmed. The blowing solution is valid for , after which the flow is unsymmetrical about . The analytical results are compared with full numerical solutions for the drag coefficient and the fraction of drag due to viscous stresses. The predictions show good agreement for and .
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