Global linear analysis of a jet in cross-flow at low velocity ratios

Chauvat, Guillaume; Peplinski, Adam; Henningson, Dan S.; Hanifi, Ardeshir

doi:10.1017/jfm.2020.85

Cited by 14 publications

(16 citation statements)

References 21 publications

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“…2014; Chauvat et al. 2020) or, for oscillating flows, the use of time-averaged data (Hammond & Redekopp 1997). In fact, unsteady flows are notoriously challenging to analyse and progress in the understanding of their linear stability characteristics has been slow (Schmid & Henningson 2001).…”

Section: Introductionmentioning

confidence: 99%

“…2009 b ; Babaee & Sapsis 2016; Chauvat et al. 2020). In more subtle scenarios, where a more detailed analysis of the spatial distribution and evolution of specific instabilities is of interest but these instabilities may not be the most prominent ones, the consideration of the full physical domain is prohibitive and might highlight other instability regions than those of interest.…”

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confidence: 99%

“…It is well known that eigenvalue spectra are sensitive to simulation details, such as the boundary conditions, but also other numerical parameters such as grid spacing and box size (Chauvat et al. 2020). The implications are not as severe for the OTD method as might seem at first glance since the dominant modes typically show the least sensitivity to the numerical parameters.…”

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confidence: 99%

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Transient linear stability of pulsating Poiseuille flow using optimally time-dependent modes

et al. 2021

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Time-dependent flows are notoriously challenging for classical linear stability analysis. Most progress in understanding the linear stability of these flows has been made for time-periodic flows via Floquet theory focusing on time-asymptotic stability. However, little attention has been given to the transient intracyclic linear stability of periodic flows since no general tools exist for its analysis. In this work, we explore the potential of using the recent framework of the optimally time-dependent (OTD) modes (Babaee & Sapsis, Proc. R. Soc. Lond. A, vol. 472, 2016, 20150779) to extract information about both the transient and the time-asymptotic linear stability of pulsating Poiseuille flow. The analysis of the instantaneous OTD modes in the limit cycle leads to the identification of the dominant instability mechanism of pulsating Poiseuille flow by comparing them with the spectrum and the eigenmodes of the Orr–Sommerfeld operator. In accordance with evidence from recent direct numerical simulations, it is found that structures akin to Tollmien–Schlichting waves are the dominant feature over a large range of pulsation amplitudes and frequencies but that for low pulsation frequencies these modes disappear during the damping phase of the pulsation cycle as the pulsation amplitude is increased beyond a threshold value. The maximum achievable non-normal growth rate during the limit cycle was found to be nearly identical to that in plane Poiseuille flow. The existence of subharmonic perturbation cycles compared with the base flow pulsation is documented for the first time in pulsating Poiseuille flow.

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Section: Introductionmentioning

confidence: 99%

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confidence: 99%

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confidence: 99%

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Transient linear stability of pulsating Poiseuille flow using optimally time-dependent modes

et al. 2021

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“…Nonlinear analysis (or simulation) is required to determine whether it is super-or subcritical. Examples from fluid dynamics include the broad class of so-called flow oscillators such as the two-dimensional cylinder flow [11,18,19,108,169,180,193,194,240,272,278,279], the lid-driven and shear-driven cavity flows [17,53,179,220,240,277], the jet in crossflow [13,63,129] or the roughness-induced boundary layer flow [46,67,154].…”

Section: Hopf Bifurcationmentioning

confidence: 99%

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

Frantz¹,

Loiseau²,

Robinet³

2023

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In fluid dynamics, predicting and characterizing bifurcations, from the onset of unsteadiness to the transition to turbulence, is of critical importance for both academic and industrial applications. Different tools from dynamical systems theory can be used for this purpose. In this review, we present a concise theoretical and numerical framework focusing on practical aspects of the computation and stability analyses of steady and time-periodic solutions, with emphasis on high-dimensional systems such as those arising from the spatial discretization of the Navier-Stokes equations. Using a matrix-free approach based on Krylov methods, we extend the capabilities of the open-source high-performance spectral element-based time-stepper Nek5000. The numerical methods discussed are implemented in nekStab, an open-source and user-friendly add-on toolbox dedicated to the study of stability properties of flows in complex three-dimensional geometries. The performance and accuracy of the methods are illustrated and examined using standard benchmarks from the fluid mechanics literature. Thanks to its flexibility and domain-agnostic nature, the methodology presented in this work can be applied to develop similar toolboxes for other solvers, most importantly outside the field of fluid mechanics.

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“…When the fluid densities of the jet and crossflow are the same, the velocity ratio () of the jet velocity () to that of the crossflow () determines the overall flow characteristics (Fric & Roshko 1994; Kelso, Lim & Perry 1996; Su & Mungal 2004; Sau & Mahesh 2008; Chauvat et al. 2020). According to Mahesh (2013), the vortical structures from the jet-crossflow interaction change at a critical velocity ratio () of 1.0–2.0.…”

Section: Introductionmentioning

confidence: 99%