Secondary flows in a longitudinally grooved channel and enhancement of diffusive transport

Abstract

Flow in a longitudinally grooved channel is analysed with the primary objective of quantifying intensification of transport mechanism due to the onset of secondary flows resulting from hydrodynamic instability and amplification of unstable modes into the nonlinear regime. Considered geometry consists of a channel whose walls are fitted with sinusoidal corrugations, forming a system of longitudinal grooves parallel to the streamwise direction. Such configuration is energy efficient, because it reduces drag when compared to the smooth reference configuration and at the same time results in flow destabilization, due to travelling wave mode already at very low values of the Reynolds number ( < 102). The analysis is performed for a range of over-the-critical values of the Reynolds numbers and focuses on nonlinear flow solutions corresponding to the limit cycle to which flow transitions from a fixed-point laminar state through a supercritical Hopf bifurcation beyond which nonlinear solution is both three-dimensional and time-periodic allowing for development of complex advection patterns and consequently improved mixing. The main results of the current work are characterization of the nonlinear solutions, attained by the flow past bifurcation and for the first time illustration of changes in the diffusive transport mechanism due to nonstationary and three-dimensional form of the flow. Our analysis indicates that significant enhancement in advective transport may be attained and that it is not monotonically related to the Reynolds number, but rather, it is related to the ability of saturated flow to intensify spanwise motions. 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.