Dynamics of coherent structures in turbulent square duct flow

Abstract

The underlying flow dynamics in a turbulent flow in a periodic square duct is investigated by using the snapshot Proper Orthogonal Decomposition (POD) technique. In this study, the friction Reynolds number based on the duct width is fixed at 300. The coherent structures are identified through the spatial and temporal analysis of POD modes. Analysis of two sets of POD data is performed. In obtaining the first set, POD is performed on the combined fluctuating velocity vector, while for the second set, only the fluctuating velocity along the y- or z-direction is used. It was found that the first two most energetic spatial POD modes are the streamwise-independent or non-propagating roll modes. The third and fourth most energetic modes are observed to be streamwise-dependent, propagating modes. The spatio-temporal analysis of POD modes confirms the presence of traveling waves in the square duct, and its average speed is also calculated. The POD of the second dataset showed only propagating modes, and no non-propagating modes were found. These propagating modes are also rotationally symmetric. It has been shown that there is an energy exchange between non-propagating modes and propagating modes. The flow dynamics of the first four reconstructed POD modes portray the self-sustaining turbulence mechanism in a square duct. The structures obtained from the first POD dataset reconstruction of 10% energy show well organized hairpin vortices. Furthermore, it is found that the energy content of 35% gives detailed information on the coherent structures aligned along the wavy streamwise direction.