Noise generation of fluttering flag in a free stream

Abstract

Fluttering flag in flow has been investigated for a long time from both a physical and an engineering point of view. Pioneering work on fluttering flag was performed by Fairthorne (1930) and Thoma (1939). Fairthorne measured the drag coefficients of several types of flags in a wind tunnel and found the relationship between the length of the flag and its coefficient. Subsequently, significant work has been conducted to investigate the forces acting on fluttering flags (Emmanuel et al., 2013). Hoerner (1965) and Taneda (1968) investigated the relationship between the drag of a flag and its length, and obtained different relationships from those of Fairthorne. Furthermore, Taneda (1968) found that the frequency of the oscillation of the flag depended on the Reynolds number and the mass ratio of the flag. The traveling waves on a fluttering flag were found and discussed by Sparenberg (1962). These groundbreaking works led to later research on parachutes (Lokerson, 1968), vehicles (Bourrières, 1969), projectiles (Fancett and Calyden, 1972), and rockets (Auman and Wilks, 2005). The fluttering flag remains a subject of interest for researchers. The time-averaged drag coefficients of fluttering flag were investigated and discussed in previous works (e.g., Wilk and Skuta, 2009), and a simple model was presented by Moretti (2003), which was later validated by Ristroph and Zhang (2008). More recently, the unsteady fluid force acting on a fluttering flag was measured, and the drag force and the moment around its strut were discussed from the perspective of its evolution during fluttering mode switches (Emmanuel et al., 2013). In addition, for the improvement of heat transfer, the flow-induced vibration of an inverted flag (Kim et al., 2013) has been studied by numerous researchers (Yu et al., 2017, Ryu et al., 2015, and Chen et al., 2018). Abstract An experimental study on the noise from a fluttering flag was performed in a low-noise wind tunnel. In the experiment, simultaneous measurements of noise from the flag and its motion were performed using microphones and a camera, respectively, to obtain the noise characteristics and their relation. Additionally, simultaneous measurements of noise and its displacement were performed to quantitively discuss their relation using seven laser displacement sensors. The experimental results indicated that a highly periodic noise with significant directivity in the vertical direction is generated from the flag, and the dominant frequency of the noise is linearly proportional to the inlet velocity. Additionally, the constants of proportionality are inversely proportional to the length of the flag and the square root of its thickness. The results also indicated that the downstream edge of the flag rolls up and down when significant periodic sound pressure is generated by the flow near the downstream edge of the flag. Furthermore, near the center of the downstream edge, the flag flutters at the dominant frequency of the emitted noise with high two-dimensionality. Therefore, the fluttering region was observed as the source of significant periodic noise from the flag. It is also found that the vibration of the downstream edge which brought the noise generation was caused by the strong upward or downward flow which occurs periodically.