Three-dimensional topology and dynamical modelling of vortex shedding from finite surface-mounted bluff bodies

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While the dynamically rich behaviour of fully turbulent wakes is very high dimensional, the most energetic, large scale coherent structures generated through instability processes are typically low dimensional and are thereby conducive to reduced order modeling procedures. These large scale eddies associated with the flow instability have the most anisotropic and geometry dependent topology and act as a source of kinetic energy in the cascade process, making them the most important to characterize. Dissipative small scale structure can then be modelled with reasonable accuracy by traditional means. The present study experimentally educes the coherent structures in the complex three-dimensional wake of a wall-mounted finite square-cross-section cylinder of aspect ratio h/d=4 and 8 immersed in boundary layers of thickness delta/d=0.72 and 2.6 at a Reynolds number of 12,000. Coherent structure eduction is carried out using phase averaging and a novel generalized phase averaging technique that incorporates proper orthogonal decomposition (POD) modes that are most important in the nonlinear instability saturation process. Global flow estimation and mode construction is undertaken using linear pressure-POD coefficient correlations, applicable to experimental investigations where practicality demands that subdomains of the global field are measured asynchronously. The large-scale coherent structures of the wakes investigated are analyzed in terms of their topology, their turbulent kinetic energy (amounting to roughly half the total fluctuation energy), and their influence on turbulence production. The educed coherent vortical structures are found to have either full-loop or half-loop topological structure depending on the boundary layer thickness, showing vortical connector strands connecting alternately shed vortices from either side of the obstacle. The structure provides an explanation of the dipole and quadrupole distributions of streamwise vorticity that have previously been observed in these types of three-dimensional wakes. The reduced order nonlinear Galerkin models derived for the dynamics of the coherent structures using the generalized phase average are shown to successfully account for the slow base flow transients, the instability saturation mechanism, and the excitation of the second harmonic modes.
Bourgeois, J. (2012). Three-dimensional topology and dynamical modelling of vortex shedding from finite surface-mounted bluff bodies (Doctoral thesis, University of Calgary, Calgary, Canada). Retrieved from doi:10.11575/PRISM/28435