Energy exchanges in the flow past a cylinder with a leeward control rod

Abstract

We study the energy exchanges between coherent structures and the mean flow in the wake of a cylinder in the presence of a leeward control rod using particle image velocimetry data at Reynolds number ( $Re$ ) $20\times 10^3$ . The shedding of the control rod depends on the oncoming shear layer and hence the downstream interaction of the main cylinder's and control rod's wake strongly depends on the control rod's setting angle ( $\theta$ ). In this work we study this interaction between the shedding modes from the cylinder and control rod at different $\theta$ . New secondary coherent motions with distinct characteristic frequencies appear in the flow field aside from the frequencies associated with the sheddings of the control rod, the main cylinder and its harmonics. A multiscale triple decomposition method is applied to extract the coherent modes associated with each of these frequencies, and the dynamics of the modes are studied using kinetic energy budget equations. The primary shedding modes of the control rod and main cylinder, as well as the harmonics of the main cylinder's shedding modes, are found to be primarily energised by the mean flow at this $Re$ , while the secondary modes are almost entirely energised by the primary modes, similar to the findings of Baj & Buxton (Phys. Rev. Fluids, vol. 2, issue 11, 2017, 114607) for a different multiscale flow configuration. The remarkable similarity in the energy exchange process forming the secondary coherent modes, observed in two different studies, hints at a possible universality in the formation process of these secondary structures in a multiscale flow.