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 $Re_H = 2.26\times10^5$ 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 $St_H\sim10^{-3}$ (1 Hz) based on bump height, (2) a low-frequency breathing motion of the separation zone centered at $St_{L_{\rm{sep}}}=0.068$ (13.5 Hz) where $L_{\rm{sep}}$ 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 $St_{L_{\rm{sep}}}=0.68-1.01$ (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.

Figures (16)

• Figure 1: 2D profiles of the Boeing Gaussian Bump along the two symmetry planes: $(a)$$y/H=0$ (flow from left to right); $(b)$$x/H = 0$, with annotation of Bump width $B_w$.
• Figure 2: $(a)$ Rendering of streamwise-vertical ($x$-$z$) PIV setup with coordinate system, Bump model and splitter plate in $3'\times3'$ test section [Adapted from robbins2021]; $(b)$ Streamwise-spanwise "top-down" ($x$-$y$) PIV setup [Reproduced from annamalai2022].
• Figure 3: Location and size of the three overlapping FOVs - F1, F2, and F3 ($\geq 20\%$ overlap) - along the streamwise-vertical $x$-$z$ plane that is used for all spanwise measurement planes $y/H=0,\,0.75,\,1.47$. Magenta dots show location of centreline ($y/H=0$) wall-pressure taps labelled 7-14. Streamwise location of surface concavity change at $x/H=1.65$ noted as well as position and streamwise extent of "top-down" $x$-$y$ PIV plane at $z/H=0.53$.
• Figure 4: (a) Mean $C_p$ variation over the Bump. Flow from left to right. Tap numbers labeled. Symbols along centreline $y/H=0$ represent mean (+), upstream extent (X) and downstream extent (*) of separation and downstream saddle points as determined by annamalai2022. Approximate location of critical lines overlaid, based on shear-stress wall-topolopy of williams2020. (b) Profiles of $C_p$ along centreline $y/H=0$ and off-centreline planes $y/H=\pm 1.47$, demonstrating mean symmetry. Lines joining dots drawn to assist visibility only. Locations of upstream and downstream surface-concavity change marked as vertical dashed lines with bump profile (top).
• Figure 5: Rendering of mean field from measurements collected at several PIV planes: (a) isometric and (b) birds-eye views. Mean fields from three overlapping FOVs along a single $x$-$z$ plane are stitched using linear interpolation to produce a planar composite mean field. Measurements are taken at (c) three separate side-on $x$-$z$ planes at $y/H\,=\,0,\,0.75,\,1.47$. Mean flow field for the (d) top-down, $x$-$y$ plane at $z/H\,=\,0.53$. Flow symmetry along centerline plane $y/H\,=\,0$. Contours represent streamwise mean velocity $U/U_{\infty}$. Magenta dots on wall represent pressure sensor locations. Select pressure taps are labeled.