Steady flow around and through a permeable circular cylinder.

*(English)*Zbl 1271.76332Summary: The steady flow around and through a porous circular cylinder was studied numerically. The effects of the two important parameters, the Reynolds and Darcy numbers, on the flow were investigated in details. The recirculating wake existing downstream of the cylinder is found to either penetrate into or be completely detached from the cylinder. It is also found that, contrary to that of the solid cylinder, the recirculating wake develops downstream of or within the porous cylinder, but not from the surface of it. These new findings provide additional evidence to L. G. Leal’s conclusion in [Phys. Fluids A, No. 1, 124–131 (1989)] that the appearance of recirculating wakes at finite Reynolds number is due to vorticity accumulation, but not a result of the same physical phenomena associated with separation in boundary layers in adverse pressure gradients. Also presented in the current study are the variation of the critical Reynolds number for the onset of a recirculating wake as a function of Darcy number and the variation of a newly defined parameter, the penetration depth, as a function of the Reynolds number and Darcy number.

##### MSC:

76S05 | Flows in porous media; filtration; seepage |

76D05 | Navier-Stokes equations for incompressible viscous fluids |

76D25 | Wakes and jets |

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