Two- and three-dimensional laminar flows between disks co-rotating in a fixed cylindrical enclosure

• Published in: International journal for numerical methods in fluids 1998-03, Vol.26 (5), p.581-603
• Main Authors: Iglesias, Immaculada, Humphrey, Joseph A. C.
• Format: Article
• Language: English
• Subjects: Applied sciences; disk drives; Electronics; Exact sciences and technology; Fluid dynamics; Fundamental areas of phenomenology (including applications); laminar flow; Laminar flows; Laminar flows in cavities; Magnetic and optical mass memories; numerical calculations; Optical storage systems, optical disks; Physics; rotating co-rotating disks; Storage and reproduction of information
• ISSN: 0271-2091; 1097-0363
• DOI: 10.1002/(SICI)1097-0363(19980315)26:5<581::AID-FLD665>3.0.CO;2-B

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, Ω. Two interdisk spacings are considered, corresponding to aspect ratios Γ = 0.186 and 0.279 (with Γ = H/(R2+a−R), where R2 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 are considered for various values of the Reynolds number, Re (with \documentclass{article}\pagestyle{empty}\begin{document}$ Re=\Omega R_2^2/v $\end{document}, where v is the kinematic viscosity of air). Axisymmetric calculations are first performed for both aspect ratios in the range 3858≤Re≤23 150. Fully three‐dimensional calculations are then performed for the configuration with Γ = 0.186 and Re = 23 150, and for the configuration with Γ = 0.279 and Re = 7715, 15 430 and 23 150. The axisymmetric calculations performed with Γ = 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 Γ = 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 Γ = 0.279 and Re > 7715 yield a novel, non‐unique 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. © 1998 John Wiley & Sons, Ltd.