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S. Derebail Muralidhar, B. Pier and J. Scott
Laboratoire de mécanique des fluides et d'acoustique, École centrale de Lyon – CNRS – Université Claude-Bernard Lyon 1 – INSA, 36 avenue Guy-de-Collongue, 69134 Écully cedex, France
Physical Review Fluids 1, 053602 (15 pages) (2016)
Stability of flow around a rotating, semi-infinite cylinder placed in an axial stream is investigated. Assuming large Reynolds number, the basic flow is computed numerically as described by Derbail Muralidhar et al. (Proc. R. Soc. London A 472, 20150850, 2016), while numerical solution of the local stability equations allows calculation of the modal growth rates and hence determination of flow stability or instability. The problem has three nondimensional parameters: the Reynolds number, Re, the rotation rate, S, and the axial location, Z. Small amounts of rotation are found to strongly affect flow stability. This is the result of a nearly neutral mode of the non-rotating cylinder which controls stability at small S. Even small rotation can produce a sufficient perturbation that the mode goes from decaying to growing, with obvious consequences for stability. Without rotation, the flow is stable below a Reynolds number of about 1060 and also beyond a threshold Z. With rotation, no matter how small, instability is no longer constrained by a minimum Re, nor a maximum Z. In particular, the critical Reynolds number goes to zero as Z→∞, so the flow is always unstable at large enough axial distances from the nose. As Z is increased, the flow goes from stability at small Z to instability at large Z. If the critical Reynolds number is a monotonic decreasing function of Z, as it is for S between about 0.0045 and 5, there is a single boundary in Z, which separates the stable from the unstable part of the flow. On the other hand, when the critical Reynolds number is non-monotonic, there can, depending on the choice of Re, be several such boundaries and flow stability switches more than once as Z is increased. Detailed results showing the critical Reynolds number as a function of Z for different rotation rates are given. We also obtain an asymptotic expansion of the critical Reynolds number at large Z and use perturbation theory to further quantify the behaviour at small S.
hal-01368877
2016b_derebailmuralidhar_prf.pdf