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ANALYSIS OF TIME-DEPENDENT VORTEX SHEDDING BY MEANS OF STREAMFUNCTIONS' STRICTLY ROTATIONAL COMPONENT
Fluid Dynamics Laboratory, Universita della Calabria, Via P. Bucci 42b, 87036 Rende (Cosenza), Italy
A computational analysis is performed on the two-dimensional time-dependent Navier–Stokes equations in their streamfunction–vorticity transport form, for a numerical investigation on vortex shedding past a circular cylinder. The numerical technique is a mixed spectral-finite analytic scheme in which the flow fields are expanded in the Fourier series along the azimuthal direction and the convolutions arising from the convective terms of the vorticity transport equation are calculated by means of Fast Fourier Transform algorithms; the time advancement is performed by using a fourth-order Runge–Kutta scheme (first four iterations) and a Predictor–Corrector algorithm (subsequent iterations). The flow of a viscous incompressible fluid around an impulsively started circular cylinder at Reynolds number Re = 1000 (based on free stream velocity and cylinder diameter) is examined with particular concern to the mechanism of vortex shedding and more particularly to the shedding of the viscous part of the flow field, when separated from the inviscid. The nonsymmetric configuration of the wake is promoted by imposing at the nondimensional time t = 0 an initial perturbation to the initially irrotational flow. The perturbation consists in a slightly rotational field implemented into the computational code by means of an appropriate perturbation function; six different perturbations are tested. The results are presented for several time steps of integration, in terms of streamlines generated by the strictly rotational component of the streamfunction. The mutual interaction of the primary vortices in the near wake as a fundamental mechanism of the "viscous" vortex shedding, is demonstrated; moreover, different perturbations induce vortex shedding phenomena with different characteristics.
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