Influence of flow confinement on the drag force on a static cylinder

The influence of confinement on the drag force F on a static cylinder in a viscous flow inside a rectangular slit of aperture h0 has been investigated from experimental measurements and numerical simulations. At low enough Reynolds numbers, F varies linearly with the mean velocity and the viscosity, allowing for the precise determination of drag coefficients λ∥ and λ⊥ corresponding, respectively, to a mean flow parallel and perpendicular to the cylinder length L. In the parallel configuration, the variation in λ∥ with the normalized diameter β=d/h0 of the cylinder is close to that for a two-dimensional (2D) flow invariant in the direction of the cylinder axis and does not diverge when β=1. The variation in λ∥ with the distance from the midplane of the model reflects the parabolic Poiseuille profile between the plates for β⪡1 while it remains almost constant for β∼1. In the perpendicular configuration, the value of λ⊥ is close to that corresponding to a 2D system only if β⪡1 and/or if the clearance between the ends of the cylinder and the side walls is very small: in that latter case, λ⊥ diverges as β→1 due to the blockage of the flow. In other cases, the side flow between the ends of the cylinder and the side walls plays an important part to reduce λ⊥: a full three-dimensional description of the flow is needed to account for these effects.