Spatio-temporal dynamics of turbulent separation bubbles

Abstract

The spatio-temporal dynamics of separation bubbles induced to form in a fully-developed turbulent boundary layer (with Reynolds number based on momentum thickness of the boundary layer of 490) over a flat plate are studied via direct numerical simulations. Two different separation bubbles are examined: one induced by a suction-blowing velocity profile on the top boundary and the other, by a suction-only velocity profile. The latter condition allows reattachment to occur without an externally imposed favorable pressure gradient and leads to a separation bubble more representative of those occurring over airfoils and in diffusers. The suction-only separation bubble exhibits a range of clearly distinguishable modes including a high-frequency mode and a low-frequency "breathing" mode that has been observed in some previous experiments. The high-frequency mode is well characterized by classical frequency scalings for a plane mixing layer and is associated with the formation and shedding of spanwise oriented vortex rollers. The topology associated with the low-frequency motion is revealed by applying dynamic mode decomposition to the data from the simulations and is shown to be dominated by highly elongated structures in the streamwise direction. The possibility of Görtler instability induced by the streamwise curvature on the upstream end of the separation bubble as the underlying mechanism for these structures and the associated low frequency is explored.

Measurements of pressure and velocity fluctuations in a family of turbulent separation bubbles

“…Again, this is fully consistent with the spectral analysis of the pressure data presented in figure 10 and confirms the presence of a low-frequency breathing mode for frequencies below 10 Hz, the intensity of which increases with the size of the TSB. This effect of TSB size is consistent with the recent DNS of Wu et al (2020), who observed a much larger variation of the reverse-flow area for a large TSB generated with a suction-only boundary condition than for a smaller TSB obtained using suction and blowing.

Figure 14.First, second and third POD modes of longitudinal velocity in the Medium TSB (arbitrary scale).

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“…presented in figure 10 and confirms the presence of a low-frequency breathing mode for frequencies below 10 Hz, the intensity of which increases with the size of the TSB. This effect of TSB size is consistent with the recent DNS of Wu et al (2020), who observed a much larger variation of the reverse-flow area A xy (t) for a large TSB generated with a suction-only boundary condition than for a smaller TSB obtained using suction and blowing. Based on these new results, it would be of interest to plot the streamwise distribution of the fluctuating pressure coefficient for frequencies above 10 Hz only, as this would remove the pressure signature of the low-frequency breathing motion.…”

“…The relevance of the first POD mode for studies of large-scale unsteadiness in TSBs was recently confirmed by Fang & Tachie (2019), who demonstrated that its time coefficient a 1 (t) is well synchronized with the time history of the total reverse-flow area A xy (t) = x,y −sign(U(t)) dx dy. The latter indicator has been used by Pearson, Goulart & Ganapathisubramani (2013) and Wu et al (2020) as a simple parameter that measures the large-scale unsteadiness in separation bubbles. A xy is most relevant for TSBs that feature large regions of instantaneous back flow at all time.…”

“…In a recent contribution, Wu, Meneveau & Mittal (2020) compared the spatio-temporal dynamics of TSBs generated by either suction-and-blowing or suction-only boundary conditions via DNS. They confirmed the presence of a low-frequency breathing motion in a very long TSB generated with the suction-only set-up but not in the smaller TSB obtained using the suction-and-blowing condition.…”

Periodic forcing of a large turbulent separation bubble

“…The separation of a turbulent boundary layer from a wall is accompanied by pressure and velocity fluctuations in a broad range of time scales. In turbulent separation bubbles (TSBs), where the separated shear layer reattaches to the wall downstream of the detachment region, at least three frequency ranges are typically observed: a low-frequency unsteadiness, usually dubbed flapping or breathing of the separation bubble, medium-frequency fluctuations, typically referring to the convection and shedding of coherent structures downstream of the separated zone, and high-frequency fluctuations related to the turbulent nature of the flow (Kiya & Sasaki 1983; Cherry, Hillier & Latour 1984; Hudy, Naguib & Humphreys 2003; Mohammed-Taifour & Weiss 2016; Wu, Meneveau & Mittal 2020).…”