Features of wavy vortices in a curved channel from experimental and numerical studies

Abstract

Evidence of time-dependent, wavy vortex motions associated with undulating and twisting Dean vortices is obtained experimentally in a curved channel with 40 to 1 aspect ratio, and mild curvature (radius ratio=0.979). These results are compared with direct numerical simulations of the time-dependent, three-dimensional Navier–Stokes equations using periodic boundary conditions in the spanwise and streamwise directions. When viewed in cross section, experimental visualizations of undulating and twisting vortex flows show rocking motion and changes in the direction of the flow between vortices that are like those observed in the simulations. Experimental spectra show that undulating vortices are replaced by the higher-frequency, shorter streamwise wavelength twisting vortices at higher Reynolds numbers. When undulating vortices are present, experimental power spectra and visualizations give frequencies that are somewhat lower than the most unstable frequencies predicted by linear stability analysis. When twisting vortices are present, experimental power spectra give fundamental and harmonic frequencies in good agreement with simulated values and with values from linear stability analysis. Twisting is present in experimental spectra over the largest Reynolds number range in spectra measured near the concave wall within inflow regions and near the concave wall near individual vortices. Fundamental amplitudes in these spectra are strongly dependent upon Reynolds number as well as on the location within the vortex pair structure. Twisting is connected to local increases of the longitudinal Reynolds stress. Like twisting, these increases occur first near the concave surface near inflow regions as the Reynolds number increases. Distributions of time-averaged streamwise velocity, streamwise vorticity, radial vorticity, and spanwise vorticity in cross-sectional planes during twisting show good quantitative and qualitative agreement with simulation results. During undulation, time-averaged radial vorticity, spanwise vorticity, and streamwise velocity distributions also compare well. In general, experimental wavy vortices are somewhat less regular than the temporally and spatially periodic wavy vortices observed in the simulations, or in Taylor–Couette flow.