Numerical investigation of supercritical Taylor-vortex flow for a wide gap

Abstract

For a wide gap ( R 1 / R 2 = 0.5) and large aspect ratios L/d , axisymmetric Taylor-vortex flow has been observed in experiments up to very high supercritical Taylor (or Reynolds) numbers. This axisymmetric Taylor-vortex flow was investigated numerically by solving the Navier–Stokes equations using a very accurate (fourth-order in space) implicit finite-difference method. The high-order accuracy of the numerical method, in combination with large numbers of grid points used in the calculations, yielded accurate and reliable results for large supercritical Taylor numbers of up to 100 Ta c (or 10 Re c ). Prior to this study numerical solutions were reported up to only 16 Ta c . The emphasis of the present paper is placed upon displaying and elaborating the details of the flow field for large supercritical Taylor numbers. The flow field undergoes drastic changes as the Taylor number is increased from just supercritical to 100 Ta c . Spectral analysis (with respect to z ) of the flow variables indicates that the number of harmonics contributing substantially to the total solution increases sharply when the Taylor number is raised. The number of relevant harmonics is already unexpectedly high at moderate supercritical Ta . For larger Taylor numbers, the evolution of a jetlike or shocklike flow structure can be observed. In the axial plane, boundary layers develop along the inner and outer cylinder walls while the flow in the core region of the Taylor cells behaves in an increasingly inviscid manner.