Investigating stability and dynamics of inverted flags attached to a cylindrical tube

Inverted flags have captivated the attention of researchers due to their distinct behavior and post-divergence dynamics. In this study, we focused on the instability and post-divergence dynamics of an inverted flag attached to a tube in a flow impinging on its free end. A new model is proposed which captures the instability of an arbitrary aspect-ratio inverted flag attached to a tube and is validated with experimental data collected in our lab. An asymptotic approach is adopted to cover a wide range of aspect ratios and tube radius to flag length ratios. Generally, the tube increases the critical flow speed by decelerating the flow speed in the vicinity of the flag. Our experimental measurements also showed the flapping frequency increases and reaches a maximum value with increasing flow speed for the case where the tube is absent. However, the frequency remained relatively constant at the onset of flapping or declined consistently for a flag affixed to a tube. Additionally, an earlier transition to the fully deflected mode was observed in the presence of a tube.