Three-Dimensional Simulation of Taylor-Couette Flow
Flow of an incompressible, viscous fluid confined in the annulus between two concentric rotating cylinders constitutes a classical problem in modern fluid mechanics. Of particular interest are the flows that arise when the inner cylinder of radius a is steadily rotating about the central axis at angular frequency Ω while the outer cylinder of radius b is held fixed. Burkhalter & Koschmieder (1974) carried out a comprehensive set of laboratory experiments in which the quasi-steady flows were examined a sufficiently long time after impulsively rotating the inner cylinder from a state of rest. They were primarily concerned with the flows when the gap of the annulus was relatively small, i.e.,η ≡ a/b = 0.727. The principal results from their experiments were the observations regarding the dependence of the axial wavelength of these vortices on the Reynolds number for a given geometric configuration. They found that the average axial wavelength of the vortices in the bulk of the interior (excluding the vortices in the vicinity of the endwall disks) initially decreased with increasing Reynolds number Re, reaching a minimum plateau for 3 ≤ Re/Re c ≤ 4 in which Re, is the critical Reynolds number, derivable from the linear stability theory for an infinite cylinder. On the other hand, it was shown by Burkhalter & Koschmieder that, for Re/Re > 4, the axial wavelength increased with increasing Re. Recently, Neitzel (1984) performed numerical experiments for axisymmetic flows to examine the structure of the Taylor vortices under the physical conditions similar to the measurements of Burkhalter & Koschmieder. One important conclusion that emerged from Neitzel’s computations was that the axial wavelength decreased with increasing Re for Re/Re c > 4. Evidently, these resulits exhibit serious disagreements with the earlier experimental observations of Burkhalter & Koschmieder.
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