Flapping motion of a permeable flag in uniform flow

The flapping motion of a permeable square-shaped flag is studied using an incompressible smoothed particle hydrodynamics method together with a newly proposed permeable flag model. Wind tunnel experiments are also performed, and the results are compared. The present model is successful in simulating two characteristic states depending on the uniform velocity, namely the 'stretched-straight state' and the 'flapping state.' Both the oscillation periods and the tail-end trajectories quantitatively agree with the experiments. However, the bistable region, which appears in the experiments, is not seen in the computational results. Except for the high-permeability case, the flags oscillate two dimensionally and no flow separation is observed irrespective of the permeability conditions. This might be due the flexibility of the flag in which the flag can change its shape in response to the low fluid pressure acting on the surface. A pair of longitudinal vortices rotating in opposite directions is generated at both spanwise ends of the flapping flag. Their strengths vary in accordance with the instantaneous lift force. When the flag is impermeable, these longitudinal vortices are connected to the spanwise vortex shed from the trailing edge and deform into a V-shaped vortex downstream. Conversely, the longitudinal vortices generated from a permeable flag simply move downstream without reconnecting. In addition, it is found that fluid permeation takes place at the location where the work by the fluid on the flag is concentrated.