Buoyancy-Affected Flow and Heat Transfer in Asymmetrically Heated Rotating Cavities

Abstract

Finite-volume predictions are presented for the convective heat transfer rates in a rotating cavity, formed by two corotating plane disks and a peripheral shroud, and subjected to a radial outflow of cooling air. The heating of the disks is asymmetric, the air entering the cavity through a central hole in the cooler (upstream) disk. The predicted Nusselt number distributions for each disk are compared with unpublished data from the University of Sussex for dimensionless mass-flow rates in the range 2800 ⩽ Cw ⩽ 14,000 and rotational Reynolds numbers, Reθ, up to 5.2 × 106. A single-grid elliptic procedure was used with turbulent transport represented via a low-Reynolds-number k–ε model and the turbulence Prandtl number concept. In comparing the predicted and measured convective heat fluxes, it is important to consider the radiative heat exchange between the disks. This is estimated using a conventional view-factor approach based on black-body emission. Under conditions of asymmetric heating, rotationally induced buoyancy forces can exert significant effect on the flow structure, the induced motion tending to oppose that imposed by the radial outflow. Indeed, flow visualization studies have revealed that, as the rotational Reynolds number is increased (for a fixed value of Cw), the flow in the source region initially becomes oscillatory in nature, leading eventually to the onset of chaotic flow in which the usual Ekman layer structure does not persist in all angular planes. The extent to which the effects of such flow behavior can be captured by the steady, axisymmetric calculation approach used here is questionable, but it is found that the turbulence model (used previously for the prediction of heat transfer in symmetrically heated cavities) still leads to good (± 10 percent) predictive accuracy for the heated (downstream) disk. However, the predicted Nusselt numbers for the cooler (upstream) disk generally show little accord with experimental data, often signifying heat flow into the disk instead of vice versa. It is concluded that the modeling of the turbulent heat transport across the core region of the flow is erroneous, especially at high rotational Reynolds numbers: This is attributed to overestimated turbulence energy production in that region due to the action of the radial-circumferential component of shear stress (νw). Adoption of an algebraic-stress model for this shear stress is partly successful in removing the discrepancies between prediction and experiment.