Modeling of vortex-corner interaction using point vortices

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Abstract
Using point vortices, the interaction of a single vortex, as well as patterns of vortices, with a corner is examined; comparisons are made with corresponding experiments. Trajectories of a vortex swept past the corner can be well-approximated, provided that a sufficiently weak strength of the vortex is specified. Calculations show that the dimensionless amplitude of the pressure fluctuation at the corner is very sensitive to small variations of the initial position of the vortex, and relatively insensitive to variations in strength; this finding has important consequences for recently observed amplitude modulation of pressure at, and velocity near, impingement. In fact, by prescribing transversely staggered patterns of vortices upstream of the corner, determined from experimental flow visualization, the form of the time-averaged pressure and velocity spectra can be approximated. The most critical feature of these spectra, a well-defined low-frequency component(s), confirms the hypothesized mechanism associated with low-frequency modulation observed in experiments. In addition, shortcomings of this method, primarily due to distributed vorticity inherent in laboratory vortices, are pointed out.

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