Chebyshev Collocation Analysis of Axisymmetric Flow and Heat Transfer Between Counter-Rotating Disks

Abstract

Unsteady constant property flow between two counter-rotating finite disks is considered for a range of Reynolds numbers. Both disks are taken to be isothermal with an imposed temperature difference between them. The flow is assumed to be axisymmetric, and buoyancy forces are neglected. The conservation equations for momentum and energy are solved using a special Chebyshev collocation technique utilizing a pressure Poisson influence matrix approach to maintain a solenoidal velocity field. Three values of the disk angular velocity ratio, Γ = ω2 /ω1 , are considered: Γ = −1.0, −0.4, and 0.0. The flow is observed to become more complex, transitioning from steady to periodic to chaotic flow regimes as the Reynolds number is increased. The simulations are found to agree reasonably well with experimental data from the literature for Γ = −1.0 and 0.0, whereas discrepancies exist for Γ = −0.4 that are similar to those observed by others in simulations using turbulence models. The heat transfer rates between the disks are shown to increase with Reynolds number due to increasing velocities and to a lesser extent chaotic mixing over the parameter range considered.