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UBC Theses and Dissertations

Nonlinear analysis of rigid body-viscous flow interaction Pareshkumar Gordhandas, Pattani


This thesis decribes the work on extending the finite element method to cover interaction between viscous flow and a moving body. The problem configuration of interest is that of a two-dimensional incompressible flow over a solid body which is elastically supported or alternatively undergoing a specified harmonic oscillation. The problem addressed in this thesis is that of an arbitrarily shaped body undergoing a simple harmonic motion in an otherwise undisturbed fluid. The finite element modelling is based on a velocity-pressure primitive variable representation of the Navier-Stokes equations using curved isoparametric elements with quadratic interpolation for velocities and bilinear for pressure. The problem configuration is represented by a fixed finite element grid but the body moves past the grid. The nonlinear boundary conditions on the moving body are obtained by expanding the relevant body boundary terms to first order in the body amplitude ratio to approximate the velocities at the finite element grid points. The method of averaging is used to analyse the resulting periodic motion of the fluid. The stability of the periodic solutions is studied by introducing small perturbations and applying Floquet theory. Numerical results are obtained for three different body shapes, namely, (1) a square body oscillating parallel to one of its sides, (2) an oscillating circular body and (3) a symmetric Joukowski profile oscillating parallel to the line of symmetry. The latter case is considered to investigate the flow pattern around an asymmetrical body. In all cases, results are obtained for steady streaming, instantaneous velocity vectors in the fluid domain, added mass, added damping, added force and stability of the flow. A comparision is made between the numerical and published experimental steady streamlines. Very good agreement is obtained for the basic nonlinear phenomenon of steady streaming.

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