Flexible Flag Research Articles

Interaction of two tandem deformable bodies in a viscous incompressible flow

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 (Ristroph & Zhang, Phys. Rev. Lett., vol. 101, 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 104. 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 ≤ D ≤ 5.5) in a flowing viscous incompressible fluid at lower Reynolds numbers (40 ≤ Re ≤ 220) using the immersed boundary (IB) method. The dimensionless bending rigidity b and dimensionless flag mass density used in our work are as follows: 8.6 × 10−5 ≤ b ≤ 1.8 × 10−3, 0.8 ≤ ≤ 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 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 b.