Unsteady separation in vortex-induced boundary layers

Abstract

This paper provides a brief review of the analytical and numerical developments related to unsteady boundary-layer separation, in particular as it relates to vortex-induced flows, leading up to our present understanding of this important feature in high-Reynolds-number, surface-bounded flows in the presence of an adverse pressure gradient. In large part, vortex-induced separation has been the catalyst for pulling together the theory, numerics and applications of unsteady separation. Particular attention is given to the role that Prof. Frank T. Smith, FRS, has played in these developments over the course of the past 35 years. The following points will be emphasized: (i) unsteady separation plays a pivotal role in a wide variety of high-Reynolds-number flows, (ii) asymptotic methods have been instrumental in elucidating the physics of both steady and unsteady separation, (iii) Frank T. Smith has served as a catalyst in the application of asymptotic methods to high-Reynolds-number flows, and (iv) there is still much work to do in articulating a complete theoretical understanding of unsteady boundary-layer separation.

Exact theory of material spike formation in flow separation

“…This problem has been partially solved by the triple-deck theory, which models the interaction between the viscous boundary layer and the outer inviscid region (see, e.g., Sychev & Sychev (1998)). The triple-deck theory, however, like the MRS criterion, assumes an infinite Reynolds number (see also the recent reviews by Ruban et al (2011) and Cassel & Conlisk (2014)).…”

Enhanced effects from tiny flexible in-wall blips and shear flow

“…The response produces only a small disturbance from λ over the quasi-steady temporal scale (i) of §3 until a critical value λ = λ c is encountered at which stage (ii) weakly nonlinear amplification can occur ( §4), leading to strongly nonlinear evolution over the faster time scale (iii) of (2.4a-2.4d), (2.6a-2.6b). This is followed by finite-time blowup as in Smith (1988), Peridier, Smith & Walker (1991 which provokes the even faster evolution (iv) described by Davies, Bowles & Smith (2003) (see also Cassel & Conlisk (2014), Gargano, Sammartino, Sciacca & Cassel (2014)) with further restructuring and deep transition towards turbulence taking place. The time scales (i)-(iv) etc for response a are slow, fast, faster, faster, etc.…”

The role of surface vorticity during unsteady separation

“…Unsteady separation in aerodynamics is accompanied with the erratic movement of the separation point location which causes highly dynamic and unpredictable loads on airfoils. 3 Separation conditions for steady flow past a twodimensional streamlined body, as proposed by Prandtl, state that flow will separate from the surface where the skin-friction is reduced to zero and a negative pressure gradient exists. This gives an Eulerian description of the boundary layer behavior and fits well in the case of steady separation.…”

“…14 The shear layer perturbation amplitude at the point of separation is expected to have a direct effect on the eruption of near-wall vorticity away from the surface into the outer flow. 3 Despite the advances in the theoretical description of unsteady separation, there is still need for experimental analysis of the role of vorticity at the surface of an airfoil in the context of unsteady separation. Identification of the initial separation location and strength of separating shear layers is an important challenge in various engineering applications.…”