Global stability analysis and direct numerical simulation of boundary layers with an isolated roughness element

Abstract

Global stability analysis and direct numerical simulation (DNS) are used to study boundary layer flows with an isolated roughness element. The aspect ratio of the element ( $\eta$ ) is small, while the ratio of element height to displacement boundary layer thickness ( $h/\delta ^{*}$ ) is large. Both steady base flows and time-averaged mean flows are able to capture the frequencies of the primary vortical structures and mode shapes. Global stability results highlight that although the varicose instability is dominant for large $h/\delta ^{*}$ , sinuous instability becomes more pronounced as $Re_h$ increases for the thin geometry ( $\eta =0.5$ ), due to increased spanwise shear in the near-wake region. Wavemaker results indicate that $\eta$ affects the convective nature of the shear layer more than the type of instability. DNS results show that different instability mechanisms lead to different development and evolution of vortical structures in the transition process. For $\eta =1$ , the varicose instability is associated with the periodic shedding of hairpin vortices, and its stronger spatial transient growth indicated by wavemaker results aids the formation of hairpin vortices farther downstream. In contrast, for $\eta =0.5$ , the interplay between varicose and sinuous instabilities results in a broader-banded energy spectrum and leads to the sinuous wiggling of hairpin vortices in the near wake when $Re_h$ is sufficiently high. A sinuous mode with a lower frequency captured by dynamic mode decomposition analysis, and associated with the ‘wiggling’ of streaks, persists far downstream and promotes transition to turbulence. A new regime map is developed to classify and predict instability mechanisms based on $Re_{hh}^{1/2}$ and $d/\delta ^{*}$ using a logistic regression model. Although the mean skin friction demonstrates different evolutions for the two geometries, both of them efficiently trip the flow to turbulence at $Re_h=1100$ . An earlier location of a fully-developed turbulent state is established for $\eta =1$ at $x \approx 110h$ .

Effect of tabs on the shear layer dynamics of a jet in cross-flow

“…The choice to use the turbulent mean flow as the base state was motivated by a scale-separation argument to justify that the Reynolds stress terms for the modes of interest were negligible. Note that stability analysis using time-averaged mean flow has been found to underpredict growth rates, but correctly predict instability frequencies (Bagheri et al 2009;Ma & Mahesh 2022). Regan & Mahesh (2017) were able to produce Strouhal numbers which matched the direct numerical simulation (DNS) spectra and dynamic mode decomposition (DMD) of Iyer & Mahesh (2016) and the experiments of Megerian et al (2007).…”

“…Note that stability analysis using time-averaged mean flow has been found to underpredict growth rates, but correctly predict instability frequencies (Bagheri et al. 2009; Ma & Mahesh 2022). Regan & Mahesh (2017) were able to produce Strouhal numbers which matched the direct numerical simulation (DNS) spectra and dynamic mode decomposition (DMD) of Iyer & Mahesh (2016) and the experiments of Megerian et al.…”

Instabilities in the wake of an isolated cylindrical roughness element

“…Bucci et al. (2018) and Ma & Mahesh (2022).

Figure 5.Snapshot of a sinuous instability downstream of the roughness element.

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“…In the context of boundary layer tripping, the instability mechanism behind a cuboid roughness element featuring a square cross-section was investigated recently by Ma & Mahesh (2022) by means of global stability analysis and DNS. They found qualitatively similar results to Loiseau et al.…”

Krylov methods for large-scale dynamical systems: Application in fluid dynamics

“…Yet, over the past decade, the time-stepping framework has become increasingly popular and enabled the investigation of the stability properties of fully three-dimensional flows. A large body of works has focused on two configurations, namely the jet in crossflow [13,129,203] or the boundary layer flow past three-dimensional roughness elements [43,46,48,67,145,154,162,276]. The stability of lid-driven and shear-driven three-dimensional cavities with spanwise end-walls has also been investigated in [99,107,143,151,155,205].…”