The control of flow separation by periodic excitation

Shock wave/boundary layer interactions occur in a wide range of supersonic internal and external flows, and often these interactions are associated with turbulent boundary layer separation. The resulting separated flow is associated with large-scale, low-frequency unsteadiness whose cause has been the subject of much attention and debate. In particular, some researchers have concluded that the source of low-frequency motions is in the upstream boundary layer, whereas others have argued for a downstream instability as the driving mechanism. Owing to substantial recent activity, we are close to developing a comprehensive understanding, albeit only in simplified flow configurations. A plausible model is that the interaction responds as a dynamical system that is forced by external disturbances. The low-frequency dynamics seem to be adequately described by a recently proposed shear layer entrainment-recharge mechanism. Upstream boundary layer fluctuations seem to be an important source of disturbances, but the evidence suggests that their impact is reduced with increasing size of the separated flow.

Low-Frequency Unsteadiness of Shock Wave/Turbulent Boundary Layer Interactions

The interactions between turbulence events and sediment motions during bed load transport were studied by means of laser-Doppler velocimetry and high-speed cinematography. Sweeps (u′ > 0, w′ 0 w′ > 0) which contribute negatively to the bed shear stress and are relatively rare, individually move as much sediment as sweeps of comparable magnitude and duration, however, and much more than bursts (u′ 0) and inward interactions (u′ < 0, w′ < 0). When the magnitude of the outward interactions increases relative to the other events, therefore, the sediment flux increases even though the bed shear stress decreases. Thus, although bed shear stress can be used to estimate bed load transport by flows with well-developed boundary layers, in which the flow is steady and uniform and the turbulence statistics all scale with the shear velocity, it is not accurate for flows with developing boundary layers, such as those over sufficiently nonuniform topography or roughness, in which significant spatial variations in the magnitudes and durations of the sweeps, bursts, outward interactions, and inward interactions occur. These variations produce significant peaks in bed load transport downstream of separation points, thus supporting the hypothesis that flow separation plays a significant role in the development of bed forms.

Role of Near-Bed Turbulence Structure in Bed Load Transport and Bed Form Mechanics

A model to explain the low-frequency unsteadiness found in shock-induced separation is proposed for cases in which the flow is reattaching downstream. It is based on the properties of fluid entrainment in the mixing layer generated downstream of the separation shock whose low-frequency motions are related to successive contractions and dilatations of the separated bubble. The main aerodynamic parameters on which the process depends are presented. This model is consistent with experimental observations obtained by particle image velocimetry (PIV) in a Mach 2.3 oblique shock wave/turbulent boundary layer interaction, as well as with several different configurations reported in the literature for Mach numbers ranging from 0 to 5.

A simple model for low-frequency unsteadiness in shock-induced separation

Detailed measurements of flow velocity and its turbulent fluctuation were obtained over fixed, two-dimensional dunes in a laboratory channel. Laser Doppler anemometry was used to measure the downstream and vertical components of velocity at more than 1800 points over one dune wavelength. The density of the sampling grid allowed construction of a unique set of contour maps for all mean flow and turbulence parameters, which are assessed using higher moment measures and quadrant analysis. These flow field maps illustrate that: (1) the time-averaged downstream and vertical velocities agree well with previous studies of quasi-equilibrium flow over fixed and mobile bedforms and show a remarkable symmetry from crest to crest; (2) the maximum root-mean-square (RMS) of the downstream velocity values occur at and just downstream of flow reattachment and within the flow separation cell; (3) the maximum vertical RMS values occur within and above the zone of flow separation along the shear layer and this zone advects and diffuses downstream, extending almost to the next crest; (4) positive downstream skewness values occur within the separation cell, whereas positive vertical skewness values are restricted to the shear layer; (5) the highest Reynolds stresses are located within the zone of flow separation and along the shear layer; (6) high-magnitude, high-frequency quadrant-2 events (‘ejections’) are concentrated along the shear layer (Kelvin-Helmholtz instabilities) and dominate the contribution to the local Reynolds stress; and (7) high-magnitude, high-frequency quadrant-4 events occur bounding the separation zone, near reattachment and close to the dune crest, and are significant contributors to the local Reynolds stress at each location. These data demonstrate that the turbulence structure associated with dunes is controlled intrinsically by the formation, magnitude and downstream extent of the flow separation zone and resultant shear layer. Furthermore, the origin of dune-related macroturbulence lies in the dynamics of the shear layer rather than classical turbulent boundary layer bursting. The fluid dynamic distinction between dunes and ripples is reasoned to be linked to the velocity differential across the shear layer and hence the magnitude of the Kelvin-Helmholtz instabilities, which are both greater for dunes than ripples. These instabilities control the local flow and turbulence structure and dictate the modes of sediment entrainment and their transport rates.

Mean flow and turbulence structure over fixed, two-dimensional dunes: implications for sediment transport and bedform stability

This article summarizes our present understanding of the physical behavior of two-dimensional turbulent separated flows, which occur due to adverse pressure gradients around streamlined and bluff bodies. The physical behavior of turbulence is flow dependent, so detailed experimental infor­ mation is needed for understanding such flows and modeling their physics for calculation methods. An earlier review (Simpson 1 985) discussed in much detail prior experimental and computational work, and this was followed by an updated review of calculation methods only (Simpson 1 987). Here additional recent references are added to those cited in the two other works. By separation, we mean the entire process of departure or breakaway, or the breakdown of boundary-layer flow. An abrupt thickening of the rotational-flow region next to a wall and significant values of the normal­ to-wall velocity component must accompany breakaway, or otherwise this region would not have any significant interaction with the free-stream flow. This unwanted interaction causes a reduction in the performance of the flow device of interest (e.g. a loss of lift on an airfoil or a loss of pressure rise in a diffuser). It is too narrow a view to use vanishing surface shearing stress or flow reversal as the criterion for separation. Only in steady two-dimensional flow do these conditions usually accompany separation. In unsteady two­ dimensional flow the surface shear stress can change sign with flow reversal without the occurrence of breakaway_ Conversely, the breakdown of the boundary-layer concept can occur before any flow reversal is encountered. In three-dimensional flow the rotational layer can depart without the

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Roger L. Simpson

Papers

Turbulent Boundary-Layer Separation