| Popis: |
A numerical study is made of the effects of both axisymmetric and non-axisymmetric disturbances on the stability of spiral flow between rotating cylinders. If we letΩ1andΩ2be the angular speeds of the inner and outer cylinders, andR1andR2be their respective radii, then for fixed values ofη=R1/R2andμ=Ω2/Ω1, the onset of instability depends on both the Taylor numberTand the axial Reynolds numberR. HereRis based on the gap width between the cylinders and the average axial velocity of the basic flow, whileTis based on the average angular speeds of the cylinders. Using the compound matrix method, we have computed the complete stability boundary in theR,T-plane for axisymmetric disturbances withη= 0.95 andμ= 0. We find that, for sufficiently high Reynolds numbers, there are two distinct axisymmetric modes corresponding to the usual shear and rotational instabilities. We have also obtained the stability boundaries for non-axisymmetric disturbances for R ≼ 6000 forη= 0.95 and 0.77 withμ= 0. These last results are found to be in substantial agreement with the experimental observations of Snyder (1962, 1965), Nagib (1972) and Mavec (1973) in the low and moderate axial Reynolds number régimes. |
