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UBC Theses and Dissertations

Finite element analysis of periodic viscous flow in a constricted pipe Singh, Rajesh Kumar


The finite element method is extended to analyze axisymmetric periodic viscous flow in a constricted pipe. This method is used to solve the pulsatile fluid flow through an artery which may be stenosed due to impingement of extravascular masses or due to intravascular atherosclerotic plaques developed at the wall of the artery. The artery geometry is approximated as an axisymmetric channel. Blood is assumed to be a Newtonian fluid, i.e., it follows a linear relationship between the rate of shear strain and the shear stress. The numerical model uses the finite element method based on velocity-pressure primitive variable representation of the Navier-Stokes equations. Eight-noded isoparametric elements with quadratic interpolation for velocities and bilinear for pressure are used. A truncated Fourier series is used to approximate the unsteadiness of flow and a modified method of averaging is used to obtain a periodic solution. Two non-dimensional parameters are used to characterize the flow: the frequency Reynolds number R[sub w], and the steady Reynolds number R[sub e]. The pulsatile flow is modeled as a linear combination of steady, cosinusoidal and sinusoidal components. The magnitude of each component is determined by minimizing the error in approximation through Galerkin's procedure. Results are obtained for various values of R[sub w] and R[sub e] for laminar flow. Results are also presented for limiting cases and, wherever possible, numerical results thus obtained are compared with analytical and experimental results published in the literature.

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