Klettner, CA; Eames, I; (2015) Low-Reynolds-number flow past a cylinder with uniform blowing or sucking. Journal of Fluid Mechanics , 780 10.1017/jfm.2015.491.

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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∞) which has a uniform through-surface blowing component (of velocity Ub). The flow is characterized in terms of the Reynolds number Re (=2aU∞/ν, where ν is the kinematic viscosity of the fluid) and the dimensionless blow velocity Λ (=Ub/U∞). 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→0. For the strong-sucking case, the asymptotic limit, CD≈−2πΛ, is confirmed. The blowing solution is valid for Λ<4/Re, after which the flow is unsymmetrical about θ=π/2. The analytical results are compared with full numerical solutions for the drag coefficient CD and the fraction of drag due to viscous stresses. The predictions show good agreement for Re=0.1 and Λ=−5,0,5.

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