Gap instability of laminar flows in eccentric annular channels

Flow visualization has demonstrated that the critical Reynolds number for flow instability in the narrow gap of an annular channel with a diameter ratio of about 0.28 increases with increasing eccentricity e in the range 0.5 < e < 0.8. The critical Reynolds numbers in the wide gap at all eccentricities and in the narrow gap for 0 < e < 0.5 seem to be insensitive to eccentricity. These observations and comparison of the frequencies of transverse flow oscillations at different Reynolds numbers and different eccentricities demonstrate that at least two distinct instability mechanisms are present in annular flows. The one of particular interest in this work arises in narrow gaps and is attributed to the instability of the two shear layers forming on either side of the gap. Linear stability analysis demonstrated that the basic flow in concentric annuli is stable for the considered diameter ratio and range of Reynolds numbers. In contrast, the basic flow in eccentric annuli has an azimuthal variation that contains two inflection points, thus being potentially linearly unstable.