Determination of groove shape with strong destabilization and low hydraulic drag

摘要

Flow through a channel equipped with plane, longitudinal grooves is investigated. We focus on determining changes to the flow dynamics due to applied wall manipulations, especially the possibility of drag-reduction, potential for hydrodynamic destabilization and onset of secondary, nonlinear flow solutions. Considered patterns of geometrical manipulation consist of plane walled grooves of triangular, variations of trapezoidal and up to rectangular shapes and are compared with existing results obtained for channels with sinusoidal corrugations. We show that there exists a strong connection in the response of the flow system to the applied pattern of grooves with the leading Fourier component of the wall pattern. The analysis starts with undisturbed, two-dimensional flows investigated with the focus on hydraulic resistance for wide range of geometric parameters. Secondly, critical conditions for the onset of travelling wave instability are determined and compared with existing results. Thirdly, nonlinear flow solutions, obtained for flows through the geometry with lowest destabilization threshold are analyzed at supercritical conditions. Finally quantification of the diffusive transport intensification due to the kinematics of the nonlinear flow solution is attempted. It is shown that, irrespective of the groove shape, longitudinal wall patterns result in flow destabilization due to traveling wave mode already at very low values of the Reynolds number ( 10(2)). At the same time such configurations can be energy efficient since overall drag is marginally increased (or in fact reduced) and at the same time diffusive processes are intensified leading to improved mixing. Implications of this study might help in development of small-scale flow devices operating at low and moderate ranges of Reynolds number with the purpose of intensifying mixing, heat transfer or reaction of chemical or biological compounds.