DNS Study on Turbulent Transition Induced by an Interaction between Freestream Turbulence and Cylindrical Roughness in Swept Flat-Plate Boundary Layer

Abstract

Laminar-to-turbulent transition in a swept flat-plate boundary layer is caused by the breakdown of the crossflow vortex via high-frequency secondary instability and is promoted by the wall-surface roughness and the freestream turbulence (FST). Although the FST is characterized by its intensity and wavelength, it is not clear how the wavelength affects turbulent transitions and interacts with the roughness-induced transition. The wavelength of the FST depends on the wind tunnel or in-flight conditions, and its arbitrary control is practically difficult in experiments. By means of direct numerical simulation, we performed a parametric study on the interaction between the roughness-induced disturbance and FST in the Falkner–Skan–Cooke boundary layer. One of our aims is to determine the critical roughness height and its dependence on the turbulent intensity and peak wavelength of FST. We found a suppression and promotion in the transition process as a result of the interaction. In particular, the immediate transition behind the roughness was delayed by the long-wavelength FST, where the presence of FST suppressed the high-frequency disturbance emanating from the roughness edge. Even below the criticality, the short-wavelength FST promoted a secondary instability in the form of the hairpin vortex and triggered an early transition before the crossflow-vortex breakdown with the finger vortex. Thresholds for the FST wavelengths that promote or suppress the early transition were also discussed to provide a practically important indicator in the prediction and control of turbulent transitions due to FST and/or roughness on the swept wing.

Changes in the Transition Process of Roughness-Induced Crossflow Vortices due to Freestream Turbulence

“…The chordwise length L x was adjusted to capture the laminar-to-turbulent transition in the cases tested here. The numbers of grids are same as our studies (Nakagawa et al, 2023a,b) and detail descriptions for grid resolution are in Nakagawa et al (2023b). The spanwise computational domain was L z = 25.14δ * 0 , which is equal to the most unstable wavelength of the stationary CFV in the FSC boundary layer (Högberg and Henningson, 1998;Brynjell-Rahkola et al, 2017).…”

“…The damping function had the same profile as the chordwise velocity profile at the inlet, as shown in Fig. 2(d) of Nakagawa et al (2023b). The turbulent intensity (T u) is defined as…”

“…The low-frequency component is filtered from the fluctuation between ω = 0.1 ± 0.05. The high-frequency component corresponds to the high-frequency SI of Type-1, and the low-frequency component corresponds to the Type-3 SI (or low-frequency mode) (Högberg and Henningson, 1998;Nakagawa et al, 2023b). Under non-FST conditions, unsteady fluctuations are not plotted for x/δ * 0 < 280.…”

“…With employing a cylindrical roughness element that triggers the stationary CFV on a swept wing or swept flat plate, several studies investigated changes in the transition process. After inducing only stationary disturbances, CFVs grow downstream, and only high-frequency SIs cause turbulent transitions (Brynjell-Rahkola et al, 2017;Ishida et al, 2022b;Nakagawa et al, 2023b). Under conditions where the roughness height is sufficiently high, unsteady fluctuations are continuously generated from the wake of the roughness without forming CFV, resulting in a rapid turbulent transition (Kurz and Kloker, 2016;Brynjell-Rahkola et al, 2017).…”

“…The effect of unsteady fluctuations on the turbulent transition process is that they affect the wake structure of the roughness, resulting in a turbulent transition without CFV formation despite the low roughness height. In the turbulent transition process on the swept flat plate under the non-FST condition, a turbulent transition due to a hairpin vortex occurs above a roughness Reynolds number of Re kk ≈ 700 (based on roughness height and base flow velocity on the top of roughness, and definition is described in § 2) (Brynjell-Rahkola et al, 2017;Ishida et al, 2022a;Nakagawa et al, 2023b). This threshold is reduced to Re kk ≈ 300 by the presence of FST (Nakagawa et al, 2023a).…”