Scaling of separated shear layers: an investigation of mass entrainment

Abstract

We report an experimental investigation of the separating/reattaching flow over a descending ramp with a $25^{\circ }$ expansion angle. Emphasis is given to mass entrainment through the boundaries of the separated shear layer emanating from the upper edge of the ramp. For this purpose, the turbulent/non-turbulent interface and the separation line inferred from image-based analysis are used respectively to mark the upper and lower bounds of the separated shear layer. The main objective of this study is to identify the physical parameters that scale the development of the separated shear layer, by giving a specific emphasis to the investigation of mass entrainment. Our results emphasise the multiscale nature of mass entrainment through the separated shear layer. The recirculation length $L_{R}$, step height $h$ and free-stream velocity $U_{\infty }$ are the dominant scales that organise the separated flow (and related large-scale quantities as pressure distribution or shear layer growth rate) and set mean mass fluxes. However, local viscous mechanisms seem to be responsible for most of local mass entrainment. Furthermore, it is shown that large-scale mass entrainment is driven by incoming boundary layer properties, since $L_{R}$ scales with $Re_{\unicode[STIX]{x1D703}}$, and in particular by its turbulent state. Surprisingly, the relationships evidenced in this study suggest that these dependencies are established over a large distance upstream of separation and that they might also extend to small scales, at which viscous entrainment is dominant. If confirmed by additional studies, our findings would open new perspectives for designing effective separation control systems.

Mass entrainment-based model for separating flows

“…Then, the vortex entrains fluid from the recirculation region to the shear layer in a neighbourhood of the mean separation, and viceversa in a neighbourhood of the mean reattachment point (represented with red arrows in Figure 1). This is exactly the general description of the backflow provided by Chapman et al [28] and Stella et al [5], so thatṁ * R seems to be related to the amount of mass put in rotation by the vortex. All in all, the spanwise vortex seems to be representative of the main topological features of the mean flow, in particular L * R , and to coherently includeṁ * R in the picture.…”

“…By considering S * R ≈ L * R and plugging in Eq. 14, simple manipulations lead to: [5]. Since the two works share the same ramp profile and have similar expansion ratios, it seems more likely that k m,L mostly depends on geometry.…”

“…Let us consider Figure 1, which shows the streamline representation of the mean flow investigated in this study. This is a massive turbulent separation, developing behind a descending ramp geometrically similar to the one used in Stella et al [5]. In contrast with that study, however, in the present experiment L * R can be forced with a rack of synthetic jets, as done in Berk et al [22].…”

“…8. Anyway, results reported by Stella et al[5] for the Correlation between L * R and b * ≈ |−1 − y * V |. The grayscale indicates the value of StA and the dashed line ( ) represents a linear best-fit of available data.…”

“…[5] a variation of almost half a decade of Re θ leads to a reduction of L * R of only 20 %, and to modifications of mean flow topology which are mild, at least in the perspective of assessing the vortex model.A more efficient, alternative approach consists in artificially tuning the properties of the flow with an external Frequency response of the synthetic jet peak velocity U * J P (• ) and of the backflowṁ * R ( ).…”