IMPULSIVELY STARTED FLOW PAST ELLIPTIC CYLINDERS: A NUMERICAL STUDY (FINITE DIFFERENCE, FOURIER SERIES, FLUID MECHANICS)
Abstract
The stream function-vorticity formulation of the equations governing the two dimensional, incompressible flow past an impulsively started ellipse are integrated numerically. The periodic coordinate of the flow variables is expanded in truncated Fourier series while the remaining spatial coordinate is discretized using finite difference schemes. The Fourier series expansions lead to analytic formulation of the spatial dependence of the stream function coefficients and to an integral relation used for the wall vorticity determination. The vorticity transport equation yields the time derivative formulation of the vorticity coefficient used in the time stepping procedure. Fast algorithms are used to perform the convolutions arising from the convective terms. Second order accuracy is achieved for time discretization and third order accuracy for the spatial discretization. An asymmetric flow condition past an ellipse at an angle of attack reveals the patterns involved in the Kutta condition establishment and clarifies the correlation existing between the flow patterns in the vicinity of the cylinder and the extrema of the lift coefficient. Moderate Reynolds number simulations reveal the patterns of time dependent complex flow configurations existing in the vicinity of the ellipse surface.
Degree
Ph.D.
Subject Area
Mechanical engineering
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