On the mixing enhancement in annular flows

The potential for mixing enhancement associated with the use of axisymmetric ribs in annular flows has been analyzed. The enhancement relies on the use of streamwise vortices produced by the centrifugal instability. Conditions leading to the formation of such vortices have been established for a wide range of geometric parameters of interest using linear stability theory. It has been demonstrated that vortices can be formed only in the presence of ribs with O(1) wavelengths. Slopes of the bounding walls in the case of the long wavelength ribs are too small to create centrifugal forces sufficient for flow destabilization. In the case of short wavelength ribs, the slopes become excessively large, resulting in the stream moving away from the wall and becoming rectilinear and, thus, reducing the magnitude of the centrifugal force field. It has been shown that decreasing the annulus' radius reduces the critical Reynolds number when ribs are placed at the inner cylinder but increases when the ribs are placed at the outer cylinder. The onset of the shear-driven instability has been investigated as the resulting travelling waves may interfere with the formation of vortices. It has been shown that the axisymmetric waves play the critical role for annuli with large radii while the spiral waves play the critical role for annuli with small radii. The ribs always reduce the critical Reynolds number for the travelling waves when compared with the onset conditions for smooth annuli. The conduit geometries giving preference to the formation of vortices while avoiding creation of the travelling waves have been identified. It is demonstrated that predictions of flow characteristics determined through the analysis of sinusoidal ribs provide a good approximation of the flow response to ribs of arbitrary shape.