Flow separation and turbulence production over trapezoidal protrusions

Abstract

The influence of rear-face inclination on turbulence around a surface-mounted protrusion depends on the separated flow approaching its trailing edge. This dependence is examined experimentally using stereoscopic particle image velocimetry over twelve trapezoidal protrusions with upper-surface length-to-height ratios $L/h=1,2,3,4$ and rear-face angles of $30^\circ$, $45^\circ$, and $90^\circ$. Measurements were conducted at a height-based Reynolds number of approximately $5\times10^4$, with an incoming boundary-layer thickness comparable to the protrusion height. For $L/h=1$ and 2, a connected reverse-flow region extends over the upper surface into the wake. For $L/h=3$ and 4, upper-surface reattachment separates the two regions. Length governs this change in topology and the variation in turbulence levels at common spatial locations, whereas rear-face inclination has its strongest influence close to the surface. From $L/h=2$ onward, shallower faces have higher near-face turbulent kinetic energy, while vertical faces have lower energy but a larger spanwise fraction. A decomposition of the in-plane deviatoric production separates the effects of Reynolds-stress and mean-strain magnitudes from those of their relative principal-axis orientation. At the inclined faces, this contribution changes from negative to positive between $L/h=1$ and 2, before upper-surface reattachment occurs. Its subsequent increase with length is driven mainly by increasing tensor magnitudes, with the largest contribution at $L/h=4$ and $30^\circ$, where strong production remains close to the rear face. These results show that local turbulence production depends jointly on the flow state approaching the trailing edge and the position of the energetic shear layer relative to the rear surface.