Simulation of the flow past an impulsively started cylinder using a discrete vortex method

Citation

Pepin, Francois Michel (1990) Simulation of the flow past an impulsively started cylinder using a discrete vortex method. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/7svd-7213. https://resolver.caltech.edu/CaltechETD:etd-08162005-104131

Abstract

NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document. Vortex methods are a powerful tool for the simulation of incompressible flows at high Reynolds number. They rely on a discrete Lagrangian representation of the vorticity field to approximately satisfy the Kelvin and Helmholtz theorems which govern the dynamics of vorticity for inviscid flows. A time splitting technique can be used to include viscous effects. The diffusion equation is considered separately after convecting the particles with an inviscid vortex method. In this thesis, the viscous effects are represented by the so-called deterministic method. The approach was extended to problems where a flux of vorticity is used to enforce the no-slip boundary condition. The ability of such a scheme to create the right amount of vorticity at the wall and to adequately redistribute it within the fluid is demonstrated by simulating the viscous flow induced by an oscillating cylinder. In order to accurately compute the viscous transport of vorticity, gradients need to be well resolved. As the Reynolds number is increased, these gradients get steeper and more particles are required to achieve the requisite resolution. In practice, the computing cost associated with the convection step dictates the number of vortex particles and puts an upper bound on the Reynolds number that can be simulated with confidence. That threshold can be increased by reducing the asymptotic time complexity of the convection step from [...] to [...]. The near-field of every vortex particle is identified. Within that region, the velocity is computed by considering the pairwise interaction of vortices. The speed-up is achieved by approximating the influence of the rest of the domain, the far-field. In that context, the interaction of two vortex particles is treated differently depending on their spatial relation. The resulting computer code does not lend itself to vectorization but has been successfully implemented on concurrent computers. The combination of a fully viscous vortex method with a fast parallel algorithm is used to simulate the flow past an impulsively started cylinder. Experiments have shown that this flow is characterized by the presence of a secondary eddy within the main recirculating region. The secondary structures over a wide range of Reynolds number (Re=550 to 9500). It was observed that the secondary phenomenon can lead to a major flow reorganization by drastically altering the transport of vorticity. The separating boundary layer acts as a source of vorticity and, at Re=550, the resulting vortex sheet smoothly rolls up into the primary vortex. For Re=3000 and 9500, however, the secondary eddy interferes with that process and the flux of vorticity is redirected toward the cylinder where it accumulates into a new vortical structure. The impulsive start is followed by a [...] singularity in the drag coefficients. The numerical simulations captured this behavior and the computed drag history for short times is in close agreement with the one predicted by a matched asymptotics analysis.

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