On turbulent separation in the flow past a bluff body

Abstract

The basic model problem of separation as predicted by the time-mean boundary-layer equations is studied, with the Cebeci-Smith model for turbulent stresses. The changes between laminar and turbulent flow are investigated by means of a turbulence ‘factor’ which increases from zero for laminar flow to unity for the fully turbulent regime. With an attached-flow starting point, a small increase in the turbulence factor above zero is found to drive the separation singularity towards the trailing edge or rear stagnation point for flow past a circular cylinder, according to both computations and analysis. A separated-flow starting point is found to produce analogous behaviour for the separation point. These findings lead to the suggestion that large-scale separation need not occur at all in the fully turbulent regime at sufficiently high Reynolds number; instead, separation is of small scale, confined near the trailing edge. Comments on the generality of this suggestion are presented, along with some supporting evidence from other computations. Further, the small scale involved theoretically has values which seem reasonable in practical terms.

Break-away separation for high turbulence intensity and large Reynolds number

“…Sychev 1972;Smith 1977;Sychev et al 1998). However, it is well-accepted that turbulent boundary layers are less prone to separate than laminar ones, which substantiates the present approach, referred to as 'non-smooth' separation by Neish & Smith (1992), in allusion to the singular behaviour of the curvature of S given by (3.9b). That is, we anticipate that one cannot determine the actual value of k and, in turn, the position of D without having gained a considerably deeper insight in the interplay of the boundary layer and the large-scale separated-flow structure.…”

“…A local description of the separation process was attempted systematically in interesting original works by Sychev & Sychev (1980), Sychev (1983) and Sychev (1987), Melnik (1989). For further references and a discussion of these enthralling and illuminating attempts, see Neish & Smith (1992) and Scheichl & Kluwick (2008a). In a recent development (Scheichl, Kluwick & Alletto 2008;Scheichl & Kluwick 2008b), a self-consistent flow structure matching the boundary layer region with the small region of pronounced laminar-turbulent transition near the leading edge of the obstacle is found to agree with the classical picture of a two-tiered turbulent boundary layer.…”

“…It should be mentioned that the assumption k 1 refers to separation asymptotically close to T where u 0D becomes asymptotically small (see figure 2a). This limiting scenario has been first addressed by Neish & Smith (1992) and critically reviewed by Scheichl & Kluwick (2008a), at least for the case of a fully developed turbulent boundary layer immersed in fully attached potential flow, here recovered in the formal limit k −1 = 0 under the premise (1.1).…”

“…In the setting of the original formulation of boundary layer turbulence by Neish & Smith (1992), which also covers underdeveloped turbulence, the Reynolds shear stress in the boundary layer is written as…”

“…This type of 'transitional' boundary layer flow was originally proposed by Neish & Smith (1992). In its form adopted here, two asymptotically small perturbation parameters are employed: a measure for the velocity defect, , and a further measure, σ , for the boundary layer thickness, denoted by δ.…”