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Interaction of two tandem deformable bodies in a viscous incompressible flow. (English) Zbl 1183.76709

Summary: Previous laboratory measurements on drag of tandem rigid bodies moving in viscous incompressible fluids found that a following body experienced less drag than a leading one. Very recently a laboratory experiment [L. Ristroph and J. Zhang, Phys. Rev. Lett. 101, 194502 (2008)] with deformable bodies (rubble threads) revealed just the opposite - the leading body had less drag than the following one. The Reynolds numbers in the experiment were around \(10^{4}\). To find out how this qualitatively different phenomenon may depend on the Reynolds number, a series of numerical simulations are designed and performed on the interaction of a pair of tandem flexible flags separated by a dimensionless vertical distance \((0 \leqslant D \leqslant 5.5)\) in a flowing viscous incompressible fluid at lower Reynolds numbers \((40 \leqslant Re \leqslant 220)\) using the immersed boundary (IB) method. The dimensionless bending rigidity \(\hat K_b\) and dimensionless flag mass density \(\hat M\) used in our work are as follows: \(8.6 \times 10^{-5} \leqslant \hat K_b \leqslant 1.8 \times 10^{-3}, 0.8 \leqslant \hat M \leqslant 1.0\). We obtain an interesting result within these ranges of dimensionless parameters: when \(Re\) is large enough so that the flapping of the two flags is self-sustained, the leading flag has less drag than the following one; when \(Re\) is small enough so that the flags maintain two nearly static line segments aligned with the mainstream flow, the following flag has less drag than the leading one. The transitional range of \(Re\) separating the two differing phenomena depends on the value of \(\hat K_b\). With \(Re\) in this range, both the flapping and static states are observed depending on the separation distance \(D\). When \(D\) is small enough, the flags are in the static state and the following flag has less drag; when \(D\) is large enough the flags are in the constant flapping state and the leading flag has less drag. The critical value of \(D\) depends on \(\hat K_b\).

MSC:

76D99 Incompressible viscous fluids
74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)
Full Text: DOI

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