Assessment of Laminar-Turbulent Transition in Closed Disk Geometries

Abstract

Finite-difference solutions are presented for rotationally induced flows in the closed space between two coaxial disks and an outer cylindrical shroud, in which there is no superimposed flow. The solutions are obtained with an elliptic-flow calculation procedure and an anisotropic low turbulence Reynolds number k-ε model for the estimation of turbulent fluxes. The transition from laminar to turbulent flow is effected by including in the energy production term a small fraction (0.002) of the “turbulent viscosity” as calculated from a simple mixing length model. This level for the artificial energy input was chosen as that appropriate for transition at a local rotational Reynolds number of 3 × 105 for the flow over a free, rotating disk. The main focus of the paper is the rotor-stator system, for which the influence of rotational Reynolds number (over the range 105 –107 ) is investigated. Predicted velocity profiles and disk moment coefficients show reasonably good agreement with available experimental data. The computational procedure is then extended to cover the cases of corotating and counterrotating systems, with variable relative disk speed.