Calculation of turbulent convection between corotating disks in axisymmetric enclosures

Abstract

A numerical investigation is conducted for the case of turbulent flow in the unobstructed space between a pair of centrally clamped coaxial disks corotating in a fixed axisymmetric enclosure. The finite difference procedure of Chang et al. ( J. Heat Transfer 111, 625–632 (1989)) is extended to include a standard two-equation ( κ- ε) model of turbulence in the core of the flow. A van Driest relation, that accounts for the effects of streamline curvature and wall shear on the energy-containing length scales, is used in conjunction with Prandtl's mixing length hypothesis to model the near wall flow. The set of equations is solved assuming a constant property, circumferentially symmetric, statistically stationary flow. This approach predicts mean velocity and heat transfer results that are in good agreement with timeaveraged experimental data. The predictions reveal a flow that, in non-dimensional variables, tends to a limiting asymptotic state at high Reynolds numbers. In the absence of blowing a symmetrical pair of crossstream eddies appear near the enclosure wall the rotation of which increases with increasing disk rotational speed. High rotational speeds, in excess of 2400 rpm in the configuration studied, and small disk separations induce large values of shear and temperature (due to viscous dissipation) in the vicinity of the enclosure wall. The flow and its heat transfer characteristics can be drastically altered by the combined effects of radial and axial blowing. Specifically, it is shown that axial blowing significantly reduces the shear and heat transfer at the curved enclosure wall.