Influence of eccentricity on stability of purely elastic Dean flow

We investigate the influence of eccentricity on linear stability of purely elastic Dean flow of an Upper Convected Maxwell liquid. A pseudo-spectral C hebyshev-Fourier collocation (CFC) technique, that exploits smoothness of t he computational domain, periodicity in the azimuthal direction and exponen tial convergence characteristics of spectral approximations, is employed fo r the spatial discretization of the governing equations. Arnoldi subspace i teration technique is employed for the selective evaluation of the leading eigenvalues. The CFC method was first benchmarked successfully for two limi ting cases that correspond to Dean flow and plane Poiseuille flow. The eige nspectrum of Dean flow is shown to consist of a number of spatially and tem porally near-resonant modes with critical Deborah numbers close to each oth er, the axisymmetric and stationary eigenmode being the most dangerous, in agreement with earlier analysis [6]. Results obtained for eccentric Dean fl ow for relatively small gap width show that eccentricity, epsilon, has a no n-monotonic influence on the Linear stability of Dean flow. The critical De borah number first increases with increasing epsilon for epsilon less than or equal to 0.1 and decreases with increasing epsilon for epsilon>0.1. The critical eigenfunctions are three-dimensional and stationary with a very hi gh degree of spacial non-uniformity. They manifest as three-dimensional 'ro lls' packed closely along the circumference of the cylinders. These complex structures exhibit steep streamwise and radial gradients near the wall and in the bulk, necessitating fine spatial resolution in the computations. Po tential mechanisms of instability are discussed. (C) 2000 Elsevier Science B.V. All rights reserved.