Unsteadiness in turbulent separated flow over a three-dimensional Gaussian bump

Abstract

The unsteady separated flow over the three-dimensional Boeing Gaussian Bump is investigated at a Reynolds number based on bump height $R{e}_H=2.26\times 10^5$ using unsteady wall-pressure measurements and planar particle image velocimetry (PIV). Four major unsteady broadband phenomena spanning more than two decades in frequency are identified: (1) a very-low-frequency (VLF) spanwise motion centered at a Strouhal number of $S{t}_H\sim 10^{-3}$ (1 Hz) based on bump height, (2) a low-frequency breathing motion of the separation zone centered at $S{t}_{L_{\mathrm{sep}}}=0.068$ (13.5 Hz) where $L_{\mathrm{sep}}$ is the mean separation length, (3) a 20 Hz frequency that appears to be associated with vortex shedding from the lateral shear layers, and (4) a centreline shear-layer vortex shedding at $S{t}_{L_{\mathrm{sep}}}=0.68-1.01$ (135-200 Hz). Interestingly, while the VLF mode has a characteristic frequency of the same order to that often reported for other rectilinear bodies and hills that exhibit bistable asymmetric wake-switching, it is found that the VLF mode for this geometry exhibits a continuous spanwise meandering motion. Joint symmetric-antisymmetric proper orthogonal decomposition modal statistics from top-down PIV data further show that the spanwise meandering and streamwise stretching of the wake -- likely associated with the breathing motion -- are dynamically coupled, with the separation zone reaching its greatest streamwise extent when in a symmetric state. In this paper, the observed hierarchy of spectral features is comparable with those observed for a wide range of geometries, suggesting connections between geometric lengthscales and the low-frequency dynamics.

arXiv comment34 pages, 16 figures, 3 supplementary movies. Submitted to Journal of Fluid Mechanics