LST and the Eigenfunction Expansion Method for Linearized Navier-Stokes Equations -- a Summary

Tumin, Anatoli

doi:10.2514/6.2020-0105

Cited by 8 publications

(4 citation statements)

References 50 publications

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“…It is particularly important to understand how modes F and S couple (synchronize) with the other branches of the spectrum (SA, FA, entropy and vorticity waves) because it can lead to the emergence of unstable modes that play a major role in triggering the transition of the boundary-layer flow. Mode coupling can occur, for example, due to non-parallel mean flow effects (Tumin 2020;Saikia et al 2022).…”

Section: Spectral Properties Of 3-d Disturbance Flow Fieldmentioning

confidence: 99%

Biorthogonal decomposition of the disturbance flow field generated by particle impingement on a hypersonic boundary layer

A. Al Hasnine,

Russo,

Tumin

et al. 2023

J. Fluid Mech.

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The disturbance flow field in a hypersonic boundary layer excited by particle impingement was investigated with a focus on the first stage of the laminar-to-turbulent transition process, namely the receptivity process. A previously validated direct numerical simulation approach adopting disturbance flow tracking is used to simulate the particle-induced transition process. Particle impingement generates a highly complex disturbance flow field that can be characterised by a wide range of frequencies and wavenumbers. After providing some insight about the spectral characteristics of the disturbance flow field in the frequency and wavenumber domains, biorthogonal decomposition is employed to reveal the composition of the disturbance flow field consisting of different continuous and discrete eigenmodes that are triggered through particle impingement. The disturbance flow characteristics for different frequency and wavenumber pairs are discussed where large contributions in the disturbance flow spectrum are observed in the vicinity of the impingement location. A significant amount of the disturbance energy is diverted into the free stream leading to large coefficients of projection for the slow and fast acoustic branches while contributions to the entropy and vorticity branches are negligible. In addition to the continuous acoustic spectra, the first-, second- and other higher-order Mack modes are activated and provide large contributions to the disturbance flow field inside the boundary layer. Finally, it is demonstrated that the disturbance flow field in the vicinity of the impingement location can be reconstructed with a maximum relative error of $2.3\,\%$ by employing a theoretical biorthogonal eigenfunction system expansion and by considering contributions from fast and slow acoustic waves and at most four discrete modes only.

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Section: Spectral Properties Of 3-d Disturbance Flow Fieldmentioning

confidence: 99%

Biorthogonal decomposition of the disturbance flow field generated by particle impingement on a hypersonic boundary layer

A. Al Hasnine,

Russo,

Tumin

et al. 2023

J. Fluid Mech.

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“…As mentioned by Tumin (2020), the eigenfunction expansion methods for the two-and three-dimensional problems are the natural extensions of the widely used local cases. The analysis of discrete modes is similar for both local and global cases and can be easily performed.…”

Section: Global Stability and Receptivity Of The Leading-edge Regionmentioning

confidence: 99%

“…Based on theoretical methods, such as finite-Reynolds-number methods (Choudhari 1994) and triple-deck theory (Ruban 1984), the bi-orthogonal eigenfunction system was found to be an effective tool for the local receptivity analyses (Hill 1995;Fedorov & Khokhlov 2002;Tumin 2007). Recently, a comprehensive review of this method is given by Tumin (2020). However, there exists no application of this approach to complex hypersonic flows.…”

Section: Introductionmentioning

confidence: 99%

Receptivity and stability of hypersonic leading-edge sweep flows around a blunt body

Ren

Wang

et al. 2021

J. Fluid Mech.

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“…The above eigenspectrum analysis provides a mathematical description of the behavior of instabilities. In such scenarios, where the qualitative behavior of instabilities varies in a meaningful fashion, a physics-based interpretation can provide complementary insights into key flow mechanisms 27 . For this, we adopt a Kovásznay-type framework, which decomposes fluctuations in terms of three physical components: vortical, acoustic and entropic, referred to earlier as fluidthermodynamic (FT) components.…”

Section: Iii2 Physical Nature Of Eigenmodesmentioning

confidence: 99%

Instability characteristics of cooled hypersonic boundary layers

Unnikrishnan

Gaitonde

2020

AIAA Scitech 2020 Forum

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Wall cooling has substantial qualitative and quantitative effects on the development of instabilities and subsequent transition processes in hypersonic boundary layers (HBLs). A sequence of linear stability theory, two-dimensional and non-linear three-dimensional direct numerical simulations is used to analyze Mach 6 boundary layers, with wall temperatures ranging from near-adiabatic to highly cooled conditions, where the second-mode instability is accompanied by radiation of energy. Decomposition of linear stability modes into their fluid-thermodynamic (acoustic, vortical and thermal) components shows that this radiation comprises both acoustic as well as vortical waves. Furthermore, in these cases, 2D simulations show that the conventional "trapped" nature of second-mode instability is ruptured. A quantitative analysis indicates that although the energy efflux of both acoustic and vortical components increases with wall-cooling, the destabilization effect is much stronger and no significant abatement of pressure perturbations is realized. The direct impact of these mechanisms on the transition process itself is examined with high-fidelity simulations of three-dimensional second-mode wavepacket propagation. In the near-adiabatic HBL, the wavepacket remains trapped within the boundary layer and attenuates outside the region of linear instability. However, wavepackets in the cooled-wall HBLs amplify and display nonlinear distortion, and transition more rapidly. The structure of the wavepacket also displays different behavior; moderately-cooled walls show bifurcation into a leading turbulent head region and a trailing harmonic region, while highly-cooled wall cases display lower convection speeds and significant wavepacket elongation, with intermittent spurts of turbulence in the wake of the head region. This elongation effect is associated with a weakening of the lateral jet mechanism due to the breakdown of spanwise coherent structures. These features have a direct impact on wall loading, including skin friction and heat transfer. In moderately cooled-walls, the spatially-localized wall loading is similar to those in near-adiabatic walls, with dominant impact due to coherent structures in the leading turbulent head region. In highly-cooled walls, the elongated near-wall streaks in the wake region of the wavepacket result in more than twice as large levels of skin friction and heat transfer over a sustained period of time.

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LST and the Eigenfunction Expansion Method for Linearized Navier-Stokes Equations -- a Summary

Cited by 8 publications

References 50 publications

Biorthogonal decomposition of the disturbance flow field generated by particle impingement on a hypersonic boundary layer

Biorthogonal decomposition of the disturbance flow field generated by particle impingement on a hypersonic boundary layer

Receptivity and stability of hypersonic leading-edge sweep flows around a blunt body

Instability characteristics of cooled hypersonic boundary layers

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