Browsing by Subject "Proper orthogonal decomposition"
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Item Reduced-order Models for Computational Aeroelasticity(2013-11-08) Freno, Brian AndrewThis dissertation presents a proper orthogonal decomposition (POD) method that uses dynamic basis functions. The dynamic functions are of a prescribed form and do not explicitly depend on time but rather on parameters associated with flow unsteadiness. This POD method has been developed for modeling nonlinear flows with deforming meshes but can also be applied to fixed meshes. The method is illustrated for subsonic and transonic flows with fixed and deforming meshes. This method properly captured flow nonlinearities and shock motion for cases in which the classical POD method failed. Additionally, this dissertation presents a novel approach for assessing the number of basis functions used in POD. POD results are compared between subsonic and transonic flows for several cases. It is demonstrated that in order to determine the number of basis functions, it is better to assess the variation of individual energy values, as opposed to the cumulative energy values. Finally, for off-reference flow conditions, interpolation is performed on a tangent space to a Grassmann manifold, and the effect of interpolation order is investigated.Item Stability and turbulence characteristics of a spiraling vortex filament using proper orthogonal decomposition(2015-05) Mula, Swathi Mahalaxmi; Tinney, Charles Edmund, 1975-The stability and turbulence characteristics of a vortex filament emanating from a single-bladed rotor in hover are investigated using proper orthogonal decomposition. The rotor is operated at a tip chord Reynolds number and a tip Mach number of 218,000 and 0.22, respectively, and with a blade loading of CT /σ = 0.066. In-plane components of the velocity field (normal to the axis of the vortex filament) are captured by way of 2D particle image velocimetry with corrections for vortex wander being performed using the Γ1 method. Using the classical form of POD, the first POD mode alone is found to encompass nearly 75% of the energy for all vortex ages studied and is determined using a grid of sufficient resolution as to avoid numerical integration errors in the decomposition. The findings reveal an equal balance between the axisymmetric and helical modes during vortex roll-up which immediately transitions to helical mode dominance at all other vortex ages. This helical mode is one of the modes of the elliptic instability. While the snapshot POD is shown to reveal similar features of the first few energetic modes, the classical POD is employed here owing to the easier interpretation of the Fourier-azimuthal modes. The spatial eigenfunctions of the first few Fourier-azimuthal modes associated with the most energetic POD mode are shown to be sensitive to the choice of the wander correction technique used. Higher Fourier-azimuthal modes are observed in the outer portions of the vortex and appeared not to be affected by the choice of the wander correction technique used.