On the abrupt turbulent reattachment downstream of leading-edge laminar separation

Abstract

A theoretical investigation of unsteady marginal separations, in a classical unsteady boundary layer, is described. This suggests that the nonlinear properties of such separations may be largely responsible, at least initially, for the central features often observed experimentally in the abrupt turbulent reattachment of eddies that follow laminar separation near the leading edges of aerofoils. The theory reduces the local flow problem to the solution of a nonlinear integro-partial differential equation for the unknown scaled skin friction, which is also proportional to the decrement in displacement locally. Numerical solutions followed by linear and nonlinear analysis show that all short-length small disturbances are unstable whenever reversed flow occurs; but for sufficiently confined initial conditions the instabilities accumulate in such a way that a breakdown is forced after a finite time. In the nonlinear breakdown a double structure arises near the point of collapse, with an effective ‘shock’ taking the flow abruptly from the reversed sense just upstream to the forward sense just downstream. This predicted shock forms the suggested possible link with the sudden transition and turbulent reattachment of laminar eddies in practice, at rounded leading edges. Discussions of the turbulence effects, of the related phenomenon of dynamic stall, of other instabilities present, and of the theoretical repercussions of the work are presented also.

Effects of compressibility, pitch rate, and Reynolds number on unsteady incipient leading-edge boundary layer separation over a pitching airfoil

“…Doligalski et al [13] have reviewed some of the important studies conducted on vortex interactions and separation including dynamic stall. Smith [38,39,41] described the instability of a leading edge separation bubble and finite time breakup of the boundary layer. He found that initially unsteady developments take place over a relatively 2 Air bubble trajectories are not instantaneous streamlines in an unsteady flow.…”

Theory and computations for breakup of unsteady subsonic or supersonic separating flows

“…Concerning computations, the flow solution depends crucially on the position of laminar-turbulent transition and hence on the transition criterion used, which is often based on empiricism. Much of the literature is reviewed by Smith & Elliott (1985), who also provide a theoretical account based on unsteady marginal separation which reproduces some of the observed features. Alternative paths to stall or transition involving some unsteady separation are studied by Peridier, Smith & Walker (1991 a, b), Hoyle, Smith & Walker (1991), Smith & Bowles (1992), Smith (1993).…”

“…Alternative paths to stall or transition involving some unsteady separation are studied by Peridier, Smith & Walker (1991 a, b), Hoyle, Smith & Walker (1991), Smith & Bowles (1992), Smith (1993). Our concern likewise is with unsteady separation and transition, taking two-dimensional flow as a starting point but with less restrictive assumptions than in Smith & Elliott (1985) on the underlying separation motion. Indeed, the starting separating motion assumed here is believed to be in its most general form (Stewartson & Williams 1969, 1973 for the supersonic range; Sychev 1972, Smith 1977 for the incompressible or subsonic range).…”

Unsteady separation in vortex-induced boundary layers

“…In particular, a class of instabilities may occur once a zero shear stress point appears within the boundary layer; recall that this is also a necessary condition for the onset of the non-interactive Van Dommelen and Shen singularity according to the MRS criterion. The case in which the point of zero shear stress forms adjacent to the surface at a velocity minimum in the context of marginal separation was considered by Smith & Elliott [48]. Cowley et al [49] consider the scenario for which the zero shear stress point occurs away from the wall, and Bhaskaran et al [50] consider the transition between these two cases.…”