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Three-dimensional simulation of a flapping flag in a uniform flow

  • WEI-XI HUANG (a1) and HYUNG JIN SUNG (a1)
Abstract

A three-dimensional computational model is developed for simulating the flag motion in a uniform flow. The nonlinear dynamics of the coupled fluid–flag system after setting up of flapping is investigated by a series of numerical tests. At low Reynolds numbers, the flag flaps symmetrically about its centreline when gravity is excluded, and the bending in the spanwise direction is observed near the corners on the trailing edge. As the Reynolds number increases, the spanwise bending is flattened due to the decrease of the positive pressure near the side edges as well as the viscous force of the fluid. At a certain critical Reynolds number, the flag loses its symmetry about the centreline, which is shown to be related to the coupled fluid–flag instability. The three-dimensional vortical structures shed from the flag show a significant difference from the results of two-dimensional simulations. Hairpin or O-shaped vortical structures are formed behind the flag by connecting those generated at the flag side edges and the trailing edge. Such vortical structures have a stabilization effect on the flag by reducing the pressure difference across the flag. Moreover, the positive pressure near the side edges is significantly reduced as compared with that in the center region, causing the spanwise bending. The Strouhal number defined based on the flag length is slightly dependent on the Reynolds number and the flag width, but scales with the density ratio as St ~ ρ−1/2). On the other hand, the flapping-amplitude-based Strouhal number remains close to 0.2, consistent with the values reported for flying or swimming animals. A flag flapping under gravity is then simulated, which is directed along the negative spanwise direction. The sagging down of the flag and the rolling motion of the upper corner are observed. The dual effects of gravity are demonstrated, i.e. the destabilization effect like the flag inertia and the stabilization effect by increasing the longitudinal tension force.

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Corresponding author
Email address for correspondence: hjsung@kaist.ac.kr
References
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Type Description Title
VIDEO
Movies

Huang and Sung supplementary movie
Movie 6. A flag of H=1.0 and ¥ñ=1.0 flapping under the gravity force at Re=200: (a) Fr=0.2; (b) Fr=0.5; (c) Fr=1.0. The gravity force is directed along the negative z-axis.

 Video (8.9 MB)
8.9 MB
VIDEO
Movies

Huang and Sung supplementary movie
Movie 3. Motion of tracing particles: (a) Re=100; (b) Re=200; (c) Re=500. The particles are released at (-0.5, ¡¾0.2, ¡¾0.3) with a time interval of 0.05.

 Video (8.6 MB)
8.6 MB
VIDEO
Movies

Huang and Sung supplementary movie
Movie 1. A flapping flag of H=1.0 and ¥ñ=1.0: (a) Re=100; (b) Re=200; (c) Re=500. The flow is along the positive x-axis.

 Video (9.7 MB)
9.7 MB
VIDEO
Movies

Huang and Sung supplementary movie
Movie 7. A flag of H=1.0 and ¥ñ=0.2 flapping at Re=200: (a) Fr=0; (b) Fr=0.5.

 Video (7.2 MB)
7.2 MB
VIDEO
Movies

Huang and Sung supplementary movie
Movie 2. Vortical structures shed from the flapping flag of H=1.0 and ¥ñ=1.0: (a) Re=100; (b) Re=200; (c) Re=500. The ¥ë2-criterion is used to identify the vortical structures and an isovalue of ¥ë2=-0.2 is chosen to plot the 3D contours.

 Video (8.9 MB)
8.9 MB
VIDEO
Movies

Huang and Sung supplementary movie
Movie 4. Vortical structures shed from the flapping flag of H=0.5 and ¥ñ=1.0: (a) Re=100; (b) Re=200; (c) Re=500.

 Video (8.9 MB)
8.9 MB
VIDEO
Movies

Huang and Sung supplementary movie
Movie 5. Vortical structures shed from the flapping flag of H=0.5 and ¥ñ=2.0: (a) Re=100; (b) Re=200; (c) Re=500.

 Video (8.9 MB)
8.9 MB

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