Flag In Uniform Flow Research Articles

Data-driven modelling of the regular and chaotic dynamics of an inverted flag from experiments

We use video footage of a water-tunnel experiment to construct a 2-D reduced-order model of the flapping dynamics of an inverted flag in uniform flow. The model is obtained as the reduced dynamics on a 2-D attracting spectral submanifold (SSM) that emanates from the two slowest modes of the unstable fixed point of the flag. Beyond an unstable fixed point and a limit cycle expected from observations, our SSM-reduced model also confirms the existence of two unstable fixed points for the flag, which were found by previous studies. Importantly, the model correctly reconstructs the dynamics from a small number of general trajectories and no further information on the system. In the chaotic flapping regime, we construct a 4-D SSM-reduced model that captures the system's chaotic attractor.

Numerical Simulation for Energy Harvesting of Piezoelectric Flag in Uniform Flow

Numerical Simulation for Energy Harvesting of Piezoelectric Flag in Uniform Flow

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.

Force measurement on coupled flapping flags in uniform flow

An experimental study on the coupled flapping of two identical flags arranged in parallel, tandem, and staggered positions in uniform flow was conducted in a wind tunnel. The dynamic characteristics of each flag were measured using an in-house designed balance and the flapping modes were analyzed through a high-speed video recording technique and a “Spatio-Temporal Evolution” software. For the side-by-side arrangement, the dependences of the kinematic and dynamic parameters on the flow speed and on the mutual distance were observed. The results indicated that the coupling motion and dynamics of two parallel flags in uniform flow were mainly affected by their mutual position. Significant drag reductions were observed when the flags flapped in the in-phase mode for a relatively small separation. For two flags in tandem arrangement, both the upstream and downstream flags experienced a drag reduction compared to the scenario of a single flag in the same flow. Especially, for relatively large separation the upstream flag had a smaller drag coefficient than that of the downstream one. For very small separation, the drag coefficient of the upstream flag was larger than that of the downstream one. Finally, for two flags arranged in a staggered configuration, an anomalous drag distribution was found. This work provides valuable experimental data and casts insight into the coupling mechanism of multiple flexible structures in an air flow.

Transition Mode of Two Parallel Flags in Uniform Flow

The coupled flapping of two side-by-side identical flags in uniform flow is observed experimentally and numerically. Besides the early reported stable, in-phase, and out-of-phase modes, a transition mode between the in-phase and out-of-phase modes is newly presented. Essentially different from the other modes, the flapping in this transition mode is no longer a single cycle motion. Especially, the FFT analysis of the displacement-time curve indicates that there are multiple peaks of frequency in this mode, of which the smaller value is comparable to the frequency of the in-phase mode and the larger one is close to that of the out-of-phase mode. Changing of the weights of different single cycle motions may explain the mode transition.

Role of mass on the stability of flag/flags in uniform flow

The interaction between flag/flags and fluid is studied numerically and the time-average flow in the wake is analyzed. It is found that a zero-mass flag in uniform flow can not exhibit sustained flapping which only occurs when the mass is involved, while multiple zero-mass flags with small separation settle into sustained flapping state. Furthermore, the nonzero mass is an essential condition for flag/flags to establish the sustained flapping in the case of convectively instable wake, while it is an unnecessary condition for the case of the absolutely instable wake.

Onset of instability of a flag in uniform flow

This paper numerically and analytically studies the onset of instability of a flag in uniform flow. The three-dimensional (3D) simulation is performed by using an immersed-boundary method coupled with a nonlinear finite element method. The global stability, bistability and instability are identified in the 3D simulations. The Squire's theorem is extended to analyze the stability of the fluid-flag system with 3D initial perturbations. It is found that if a parallel flow around the flag admits an unstable 3D disturbance for a certain value of the flutter speed, then a two-dimensional (2D) disturbance at a lower flutter speed is also admitted. In addition, the growth rate of 2D disturbance is larger than that of the 3D disturbance.

Flutter instability of rectangle and trapezoid flags in uniform flow

An experiment on the flutter instability of rectangle and trapezoid flags is conducted in a low speed wind tunnel and a physical model is proposed to predict the critical velocity of flutter instability of the flags. The nondimensional second moment of area is used to depict the effect of the flag shape on the flutter. The result shows that the method presented in this paper can be used to predict the lower-critical velocity. The change of the flutter envelope and critical velocity is found to be related to the dominant mode.