COMPUTATIONAL EXPERIMENTS ON THE STABILITY OF AXISYMMETRIC TAYLOR VORTEX: WAVE LENGTH SELECTION (FLUID MECHANICS, SPECTRAL METHODS, INSTABILITIES)

AHMED HAMIDI, Purdue University

Abstract

An investigation on the stability of viscous flow between concentric rotating cylinders is performed to determine the axial wave length that prevails in the Taylor vortex flow. To this end, an exact mathematical model capable of resolving axisymmetric secondary flows is derived by integrating the Navier-Stokes equations in their Fourier space form. This form is constituted by a number of non-linearly coupled ordinary differential equations in time and space dependent Fourier coefficients of stream function, azimuthal velocity, and azimuthal vorticity. The computation of the convolution sums is approached by the Fast Fourier Transform algorithm using the vectorized subroutine FFT on a CDC Cyber 205. An important feature of the model is the analytical integral solution for the spatial dependence of the stream function and the pressure coefficients. Additionally, the boundary values of the vorticity coefficients are obtained from integral relations along with values of the stream function coefficients at the boundaries of the cylinders. The finite difference scheme used for the time advancement is a fourth order predictor-corrector scheme, and a quintic spline method has given exceptionally good results for the numerical evaluation of the integrals. Details of the flow are presented for Reynolds number Re = 150, a wide gap, and outer cylinder at rest. Results from the numerical experiment compare very favorably with other published simulations. The velocity field, stream function, vorticity, angular momentum and enstrophy have been plotted frequently for the double purpose of monitoring the numerical experiment and of illustrating its results. In this study, the length of the cylinders is found to be an important factor in determining the preferred wave number.

Degree

Ph.D.

Subject Area

Civil engineering

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