Experimental study of flag fluid–structure interaction in a laminar jet and application of POD

A fluttering flag in a uniform laminar flow exhibits complex fluid–structure interaction (FSI) behavior. This investigation experimentally studied aerodynamic load behavior and its connection to the oscillation behavior, flag envelope and fluid flow parameters, and application of Proper Orthogonal Decomposition (POD) to fluid flow data to elucidate changes in flow behavior associated with the changes in oscillation modes and observed drag coefficient values. For this purpose, three flag models with varying lengths were used. The aerodynamic load forces were measured using a high-precision load cell, and two-dimensional Particle Image Velocimetry (PIV) was used to quantify the flow field around the flag. The Reynolds number ($Re$), mass ratio ($R_1$), and dimensionless rigidity ($R_2$) values were varied between $4.4\times 10^4-12.3\times 10^4$, $1.48-2.77$, and $1.3\times 10^{-3}-15.1\times 10^{-3}$, respectively. The results showed the linear relationship between drag coefficients with normalized amplitude of oscillation and Strouhal number. The results also showed the connection between observed drag and change in flag oscillation modes. The POD analysis showed that the energy content of the POD modes changed with the change in flag oscillation from mode-2 to mode-3 oscillations. The phase portrait of the first four POD modes also showed a unique interplay of POD modes, resulting in a change in the velocity flow field associated with the change in oscillation modes. The low-order reconstruction using select POD modes and control volume analysis of the velocity flow field showed a connection between POD modes and observed drag.