Large eddy simulation of turbulent heat transfer in stationary and rotating square ducts

The velocity field and the instability of the flow in a rotating square duct were investigated. The velocity profiles were obtained for Ekman numbers less than 1/16 by combining a linear Stewartson layer solution, a non-linear Ekman layer solution and a local similarity assumption. The transition of the secondary-flow pattern from one pair of vortices to two pairs of vortices was studied with the conventional linearized equations for small disturbances. The resultant sixth order equation was solved numerically. The onset of the instability of the Ekman layer was also studied and found to be relevant to the class A and class B waves. The present theory was compared with the experimental results of Smirnov and Yurkin (1983). The critical rotation numbers for marginal stability of both the Stewartson layer and the Ekman layer were found in good agreement with measurements. The experiments of Smirnov and Yurkin (1983) also revealed a boundary in the parameter space corresponding to the sudden change of the slopes of the drag curves, which was found at least partially related to the wavy instability of the Stewartson layer. A quasi-geostrophic method was used to include the effects of Ekman friction in the instability formula. The critical rotation numbers obtained were in qualitative agreement with experimental measurements. Another phenomenon the experiments discovered was the pulsation of the four-vortex pattern as a certain critical Reynolds number was exceeded. This phenomenon has not yet been explained by the present analysis.