Fluttering flags are a canonical study case in the field of fluid-structure interactions. Fluttering flags involve a flexible and elongated body, the flag, immersed in a steady flow stream. At low flow velocities, flags remain still and tend to align with the flow. For sufficiently high flow velocities, the flag does not stay static any more, and starts oscillating. The waving motion of a flag is what we refer to as flutter. The onset of flutter has received a lot of interest because it is directly linked to our capabilities to predict and avoid the catastrophic effects of large amplitude vibrations on industrially relevant systems such as wings, foils or industrial printing press. What happens once the flag has started flapping, the post-critical regime, has received less attention. This thesis focuses on the post-critical flapping response of flags of various dimensions and shapes.
Studies on the post-critical flapping regime are challenging, experimentally and numerically. We develop an experimental apparatus to gather deformation and force data for a broad range of flow velocities and flag shapes composed of rectangular, trapezoidal, polygonal and leaf-inspired flags. We also perform flow measurements for a selected number of cases. Flags flap fast, and to gather many flapping cycles for different shapes and flow velocities, we leverage novel event-based imaging techniques to efficiently record well-resolved flag deformations at mid-height. Spatially and temporally-resolved deformation data give access to the flapping length scales, time scales, and more refined quantities such as pressure difference estimates.
The effect of mass ratio, aspect ratio, and tapering is investigated with rectangular and trapezoidal flags. Rectangular flags of different aspect ratios and mass ratios show consistent variations of flapping time scales, force data and flow quantities with aspect ratios. We show that shorter flags experience an overall lower pressure difference in the post-critical regime, leading to a slower travelling wave, lower tip frequency, weaker vorticity release, and overall shorter flags experience less time-averaged drag compared to tall flags. Trapezoidal shapes are tapered. Tapering changes where the mass and stiffness is distributed along the flag, and is quantified by the radius of the second moment of area. Converging shapes are effectively stiffer, flap at a faster frequency, but experience less drag compared to diverging shapes. For both the rectangular and trapezoidal flags, we investigate which length scales work best to describe the flapping response, whether based on the centreline length, the perimeter, the planar and projected areas, or the radius of the second moment of area. We discuss different models to predict the time-averaged drag, based on tip velocities and pressure estimates.
To open up to a larger family of shapes, we test and measure the flapping response of polygonal and leaf-inspired shapes and compare the resu
