AN EXPERIMENTAL INVESTIGATION INTO CONFINEMENT EFFECTS OF INVERTED FLAGS IN A CIRCULAR TEST SECTION

Abstract

Inverted flag configurations frequently show up in piezoelectric energy harvesting applications and vortex-induced convective heat transfer enhancement. Existing studies primarily examine the dynamics of inverted flags in unconfined or weakly confined flows. Here, we investigate the hydrodynamic confinement of semicircular and rectangular inverted flags mounted in a cylindrical channel. The experiments are performed inside a square test section of a water tunnel, with a custom acrylic tube apparatus with an inner diameter, $D_H = 108$ mm, inserted to create the cylindrical boundary condition. A high-speed camera below the test section records the flag kinematics, and 2-D Particle Image Velocimetry (2-D PIV) is performed on image pairs captured at an Nd:YAG laser sheet set to the flag mid-span. Six flag setups are studied: four semicircular (1C, 2C, 3C, 4C) and two rectangular (1R, 2R), all of which were fabricated while keeping their aspect ratio ($AR \approx 8/\pi$) constant. Rectangular and semicircular inverted flags lose stability at different flow speeds due to their difference in planform geometry. A theoretical model is used to derive the critical divergence threshold for semicircular inverted flags to be $\kappa^\infty_{lower,C} \approx 3.08$, alongside the already established threshold for rectangular inverted flags of $\kappa^\infty_{lower,R} \approx 1.85$ in the literature. Both agree with the measured onset of flapping observed near $\kappa^\infty \approx 1.85$ for the rectangular flags and beyond $\kappa^\infty \approx 3.0$ for the semicircular flags. Next, these theoretical thresholds are used to normalize the experimental data to collapse the amplitude response of all the flags, revealing that the order in which flags lose stability is correlated to the spanwise confinement ratio, defined as flag height to channel diameter $H/D_H$ of each flag. As $H/D_H \rightarrow 1$, the lower divergence threshold measured approaches the 2-D theoretical prediction. It was also noted that the ratio of the lower to upper divergence limit, $\kappa_{lower}/\kappa_{upper} \approx 0.47 \pm 0.03$, remains relatively constant independent of flag size or geometry. Phase-resolved vorticity plots indicate that for larger flags, the leading edge vortices (LEVs) generated at the flag tip interact with the tube wall, resulting in the wall generating vorticity of the opposite sign. Streamwise velocities at the upstream, flag tip, and flag clamp are also analyzed to study confinement-induced near-wall flow acceleration. Mixing analysis shows that 1C and 1R have a minimal effect on wall-normal momentum transport as their trailing edge vortices (TEV) rarely reach the wall within the measured flow domain. On the contrary, flags 2C and 2R offer significantly better convective mixing across a wide streamwise length scale. Flag 2C displayed intense but short-lived mixing events, compared to the smoother and more sustained time window, but less intense than that provided by flag 2R. Because their tips are much closer to the wall, the two largest flags (3C and 4C) utilize their LEVs, coupled with secondary wall vorticity, to drive intense mixing that is superior to the rest of the flags, making them potential candidates as vortex generators for heat transfer applications.