Two- and three-dimensional laminar flows between disks co-rotating in a fixed cylindrical enclosure
✍ Scribed by Immaculada Iglesias; Joseph A. C. Humphrey
- Publisher
- John Wiley and Sons
- Year
- 1998
- Tongue
- English
- Weight
- 496 KB
- Volume
- 26
- Category
- Article
- ISSN
- 0271-2091
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✦ Synopsis
A numerical investigation is performed for the constant property laminar flow of air in the space between a pair of disks clamped co-axially on a central hub and co-rotating in a stationary cylindrical enclosure. Both two-and three-dimensional flow conditions are examined in relation to the interdisk spacing, H, and the disk angular velocity, V. Two interdisk spacings are considered, corresponding to aspect ratios G=0.186 and 0.279 (with G=H/(R 2 +a-R), where R 2 is the disk radius, a is the disk rim -enclosure wall clearance, and R is the hub radius). A range of rotational speeds encompassing the transition from axisymmetric two-dimensional steady flow to non-axisymmetric three-dimensional unsteady flow is considered for various values of the Reynolds number, Re (with Re= VR 2 2 /6, where 6 is the kinematic viscosity of air). Axisymmetric calculations are first performed for both aspect ratios in the range 3858 5 Re5 23 150. Fully three-dimensional calculations are then performed for the configuration with G = 0.186 and Re = 23 150, and for the configuration with G= 0.279 and Re= 7715, 15 430 and 23 150. The axisymmetric calculations performed with G= 0.186 confirm many known features of the flow, including the transition from a steady flow to an oscillatory periodic regime. This occurs at : Re= 23 150 for a configuration with a/H= 0, and at :Re=14 670 for one with a/H =0.28 and a finite disk thickness (b/H=0.2). Three-dimensional calculations performed for G= 0.186 with a/H = 0 and Re= 23 150 reveal a circumferentially periodic flow pattern with eight foci of intensified axial component of vorticity. The axisymmetric calculations performed with G=0.279 and Re \7715 yield a novel, nonunique steady solution for the velocity field that is asymmetric with respect to the interdisk mid-plane. No experimental verification of this finding exists to date, but similar situations are known to arise in the context of anomalous modes of the Taylor-Couette flow. Relaxing the axisymmetry constraint allows this flow to evolve to an oscillatory three-dimensional regime of increasing irregularity with increasing rotational speed. In this case, the number of foci of intensified axial vorticity varies with time, ranging from six at Re =7715 to between six and eight at Re= 23 150.