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

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.

An Improved Direct-Forcing Immersed Boundary Method for Fluid-Structure Interaction Simulations1

“…The rolling motion of the upper corner is also seen. These observations are consistent with the report in [10]. Figure 10 shows the time histories of the transverse displacements of points A in Figure 8 for Fr = 0.0.…”

“…Figure 10 shows the time histories of the transverse displacements of points A in Figure 8 for Fr = 0.0. Both the result of present study and that of Huang & Sung [10] are plotted in the figure. An excellent agreement between the two results is clearly seen.…”

“…figure 8 for Fr = 0.0. Solid line denotes the result of the present study; square denotes the result from Huang & Sung [10].…”

Flutter-driven triboelectrification for harvesting wind energy

“…Meanwhile, there has been considerable research on the basic dynamics of flexible structures like flags, which can be bent, folded, twisted or waved in the air [19][20][21][22][23][24][25][26] . The first experimental study on fluttering behaviour was performed by Taneda 27 with a flag made of various fabrics and shapes, to find a variety of flapping modes (for example, nodeless, one-node, imperfect-node and two-node flutters).…”

Coupling Motion and Energy Harvesting of Two Side-by-Side Flexible Plates in a 3D Uniform Flow

“…More recently, it was found that schooling fish can improve locomotion efficiency in side-by-side configuration [29,30]. Although most of the flexible bodies physically exist with a finite aspect ratio, only a few 3D simulations of an isolated flexible plate have been reported [31][32][33][34]. To our knowledge, the coupling motions and energy conversion performance of two side-by-side flexible plates in a 3D viscous flow have not been modeled and studied numerically yet.…”