Investigation of the roughness-induced transition: global stability analyses and direct numerical simulations

Abstract

. Investigation of the roughness-induced transition: global stability analyses and direct numerical simulations. Journal of Fluid Mechanics, Cambridge University Press (CUP), 2014, 760, pp.175-211. 10.1017/jfm.2014.589. hal-01086744 Science Arts & Métiers (SAM)is an open access repository that collects the work of Arts et Métiers ParisTech researchers and makes it freely available over the web where possible. The linear global instability and resulting transition to turbulence induced by an isolated cylindrical roughness element of height h and diameter d immersed within an incompressible boundary layer flow along a flat plate is investigated using the joint application of direct numerical simulations and fully three-dimensional global stability analyses. For the range of parameters investigated, base flow computations show that the roughness element induces a wake composed of a central low-speed region surrounded by a threedimensional shear layer and a pair of low-and high-speed streaks on each of its sides. Results from the global stability analyses highlight the unstable nature of the central low-speed region and its crucial importance in the laminar-turbulent transition process. It is able to sustain two different global instabilities: a sinuous and a varicose one. Each of these globally unstable modes are related to a different physical mechanism. While the varicose mode finds its root in the instability of the whole three-dimensional shear layer surrounding the central low-speed region, the sinuous instability turns out to be similar to the von Kármán instability in the two-dimensional cylinder wake and finds its root in the lateral shear layers of the separated zone. The aspect ratio of the roughness element plays a key role on the selection of the dominant instability. Indeed, whereas the flow over thin cylindrical roughness elements transitions due to a sinuous instability of the near-wake, for larger roughness element the varicose instability of the central low-speed region turns out to be the dominant one. Direct numerical simulations of the flow past an aspect ratio η = 1 (with η = d/h) roughness element sustaining only the sinuous instability have revealed that the bifurcation occurring in this particular case is supercritical. Finally, comparison of the transition thresholds predicted by global linear stability analyses with the von Doenhoff-Braslow transition diagram provides qualitatively good agreements.

On Reynolds number dependence of micro-ramp-induced transition

“…The symmetrical distribution of the perturbation is consistent with the varicose-type mode in the wake of roughness element obtained by stability analysis ( On Reynolds number dependence of micro-ramp-induced transition 617 periodic shedding of hairpin vortices. As reported by Loiseau et al (2014), although the varicose mode appears initially at the wake centre, it propagates spanwise and occupies the whole domain width. However, in the present POD analysis, modes 1 and 2 remain confined within a limited spanwise range (z/h = [−0.5, 0.5]).…”

“…Nevertheless, increasing both parameters leads to a fast growth of the perturbations, causing early transition. In the recent DNS study performed by Loiseau et al (2014), velocity streaks were also observed in the wake of discrete cylinders. Increasing Re h from a subcritical to supercritical value results in a longer streamwise persistence of a low-speed region around the symmetry plane.…”

“…No pair of eigenmodes arises in this case. As observed in the sinuous instability mode (Asai, Minagawa & Nishioka 2002;Loiseau et al 2014), the asymmetric mode modulates the flow into a sinuously wiggling pattern. However, as the magnitude of the asymmetric patches in mode 3 is remarkably lower than the symmetric mode (1 and 2), the sinuous modulation of the K-H vortices is not found in the instantaneous flow.…”

“…The latter can lead to the formation and growth of hairpin-like vortices in regular succession. The importance of K-H instability on the overall transition process highly depends on Reynolds number (Loiseau et al 2014). At subcritical Re h , the detached shear layer appears to remain stable with no development of unsteady vortical structures.…”

Stability and sensitivity of a cross-flow-dominated Falkner–Skan–Cooke boundary layer with discrete surface roughness

“…By increasing Re k in a two-dimensional boundary layer beyond a certain limit, Re k,t , the transition location has been noticed to move upstream to the trailing edge of the roughness (von Doenho↵ & Braslow 1961). Due to its importance for the development of laminar wings, the determination of Re k,t has been the subject of several global stability analyses (Loiseau et al 2014;Citro et al 2015;Kurz & Kloker 2016). For roughness elements in a Blasius boundary layer, the above mentioned flow-tripping was found to correspond to the onset of a global flow instability.…”