Mechanisms of flow tripping by discrete roughness elements in a swept-wing boundary layer

Abstract

The effects of a spanwise row of finite-size cylindrical roughness elements in a laminar, compressible, three-dimensional boundary layer on a wing profile are investigated by direct numerical simulations (DNS). Large elements are capable of immediately tripping turbulent flow by either a strong, purely convective or an absolute/global instability in the near wake. First we focus on an understanding of the steady near-field past a finite-size roughness element in the swept-wing flow, comparing it to a respective case in unswept flow. Then, the mechanisms leading to immediate turbulence tripping are elaborated by gradually increasing the roughness height and varying the disturbance background level. The quasi-critical roughness Reynolds number above which turbulence sets in rapidly is found to be Re kk,qcrit ≈ 560 and global instability is found only for values well above 600 using nonlinear DNS; therefore the values do not differ significantly from two-dimensional boundary layers if the full velocity vector at the roughness height is taken to build Re kk . A detailed simulation study of elements in the critical range indicates a changeover from a purely convective to a global instability near the critical height. Finally, we perform a three-dimensional global stability analysis of the flow field to gain insight into the early stages of the temporal disturbance growth in the quasi-critical and over-critical cases, starting from a steady state enforced by damping of unsteady disturbances.

Plasma virtual roughness elements for cross-flow instability control

“…The upper electrode is shown in pink, while the lower electrode is in thick black. A streamline (shown in red) is shown to indicate the upstream effect of the actuator over a smooth circular disk, as shown in a DNS study by Kurz and Kloker (2016). The torus-shaped flow structure associated with the induced flow towards the centre of the ring-type plasma actuator (see Fig.…”

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

“…The eigenfunctions consist of two di↵erent regions of spatial growth -one located immediately behind the roughness and extending to x ⇡ 100, and another region that coincides with the growth of the CF vortices and extends until the sponge region. Comparison of figure 6 to figure 29 in Kurz & Kloker (2016), shows that their eigenfunctions mainly consist of the first region, whereas the second region, which according to figure 6 becomes dominant for longer domains, in their analysis has been truncated. This could explain why their growth rates did not change significantly with the length of their rather short domains.…”

“…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. However, for swept-wing boundary layers, the situation is more complex, as recently demonstrated by Kurz & Kloker (2016). These authors carried out a comprehensive direct numerical simulation (DNS) study accompanied by a global stability analysis and noted a sensitivity of the unstable eigenvalue spectra with respect to numerical parameters and domain size.…”

“…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.…”

Roughness-induced transition by quasi-resonance of a varicose global mode

“…Note finally that similar analyses have been conducted for roughness-induced compressible boundary-layer flows. One can cite for instance the works of Bernardini, Pirozzoli & Orlandi (2012), Subbareddy, Bartkowicz & Candler (2014), Kurz & Kloker (2016) and references therein for more details.…”