Hydrodynamics of a weakly curved channel

The underlying mechanism of curvature induced helicoidal flow in a weakly curved channel intrigues researchers. Here, we explore the hydrodynamics of weakly curved channels, defined by the limiting values of the curvature ratio (ratio of channel half-width to radius of curvature) and aspect ratio (ratio of channel half-width to average flow depth) as 0.1 and 10, respectively. The three-dimensional continuity and momentum equations are solved analytically, involving the appropriate boundary conditions and closing the system by means of the turbulence closure model and the indispensable fluid constitutive formulations. The skewed filament of the azimuthal velocity component, emanating from the effects of curvilinear streamlines, is introduced into the analysis, for the first time, to address the flow asymmetry across the flow cross section. The modification of the radial slope due to the presence of the stress term in the radial momentum balance is accomplished by a slope correction factor, which turns out to be a weak function of the reciprocal of the power-law exponent. The attenuation of the azimuthal shear stress component, resulting from the skewed velocity profile, is characterized by the damping function to provide a quantitative insight into the redistribution of the primary flow momentum. The velocity field reveals that the flow circulation (on the flow cross-sectional plane) about the azimuthal axis and the flow helicity strengthen with an increase in the curvature ratio. The variation of the radial free surface profile is more sensitive to the flow Froude number than to the curvature ratio. The evolutions of the stress field with several key parameters are also examined. Published under license by AIP Publishing