Growth mechanisms of second-mode instability in hypersonic boundary layers

Tian, Xudong; Wen, Chih-Yung

doi:10.1017/jfm.2020.981

Cited by 10 publications

(10 citation statements)

References 27 publications

(37 reference statements)

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“…For hypersonic flows, porous coatings have been proven to be a promising passive control strategy for the second mode. Tian & Wen (2021) showed that the effect of the porous coating on the second mode was to distort the phase of mean temperature gradient effect at Mach 6 and reduce the internal energy growth induced by wall-normal transport. This mechanism resembles that of wall heating inferred from figure 5( b ).…”

Section: Results Of Rpamentioning

confidence: 99%

“…Figure 6 showed the effect of the porous coating on the oblique first mode at Mach 3.5. The same boundary condition as Tian & Wen (2021) is imposed, where is the wall acoustic admittance. When the wall changes from smooth () to porous (), the growth rate of the most unstable oblique first mode increases from to .…”

Section: Results Of Rpamentioning

confidence: 99%

“…Compared with the phase distribution of the smooth-wall case, a prominently enlarged region of the RSS (related to in phase) promotes the production of the streamwise velocity fluctuation. This analysis of the streamwise momentum equation was not considered in Tian & Wen (2021). For the change of internal energy, RTS (related to in phase) is slightly strengthened while the dilatation is slightly suppressed for the porous-wall case, which is consistent with Tian & Wen (2021) at Mach 6.…”

Section: Results Of Rpamentioning

confidence: 99%

“…The base spanwise velocity is set to . The governing equations of the LST, mainly the momentum equations in the and directions and the internal energy equation, can be written as (Tian & Wen 2021) where , and represent the rates of change in fluctuations of streamwise velocity, wall-normal velocity and internal energy, respectively. The right-hand side sources and represent the production by mean shear and mean temperature gradient, which are associated with Reynolds shear stress (RSS) and Reynolds thermal stress (RTS), respectively.…”

Section: Methodsmentioning

confidence: 99%

“…The phase behaviour is considered as an alternative indicator to explain the exponential energy growth of the second mode. Tian & Wen (2021) analysed the local phase difference between the rate of change of fluctuations and right-hand side source terms. The purpose was to identify the pronounced sources and explain the growth mechanisms of the second mode.…”

Section: Relative Phase Analysismentioning

confidence: 99%

See 4 more Smart Citations

A unified explanation of energy growth sources for unstable modes in flat-plate boundary layers

Chen,

Guo,

Wen

2023

J. Fluid Mech.

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The detailed energy sources that sustain the eigenmodal exponential growth in boundary layers are currently unclear. In the present study, the phase of each term in the linear stability equation is examined to identify the significant physical sources for a wide range of Mach numbers and wall temperature ratios. The Tollmien–Schlichting mode for incompressible flows, the oblique first mode for supersonic flows and the Mack second mode and supersonic mode for hypersonic flows share some similar features. The unique appearance of obliqueness for the most unstable first mode is accompanied by the enhancement of Reynolds shear stress. By contrast, the weakened Reynolds thermal stress prevents the oblique second mode from being the most unstable state. Wall cooling stabilises the oblique first mode by rendering Reynolds thermal stress and dilatation fluctuations out of phase with the internal energy fluctuation. It destabilises the second mode by a newly generated pronounced region of wall-normal internal energy transport beneath the second generalised inflection point. In comparison, the porous coating destabilises the oblique first mode by significantly enhancing the mean-shear production while it stabilises the second mode similarly to wall heating. Finally, the relatively weak supersonic mode has the feature that the phase destruction of wall-normal transport near the critical layer results in a low contribution to the internal energy growth. Connections and consistencies are also highlighted with the previous inviscid thermoacoustic interpretation for the second mode (Kuehl, AIAA J., vol. 56, 2018, pp. 3585–3592) and for the supersonic mode. The pronounced sources along the critical layer and near-wall regions provide a unified understanding of the local energy amplification mechanisms of the inviscid modes in hypersonic boundary layers.

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Section: Results Of Rpamentioning

confidence: 99%

Section: Results Of Rpamentioning

confidence: 99%

Section: Results Of Rpamentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

Section: Relative Phase Analysismentioning

confidence: 99%

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A unified explanation of energy growth sources for unstable modes in flat-plate boundary layers

Chen,

Guo,

Wen

2023

J. Fluid Mech.

Self Cite

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Instability and transition control by steady local blowing/suction in a hypersonic boundary layer

Zhuang,

Wan,

Liu

et al. 2024

J. Fluid Mech.

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The efficacy of steady large-amplitude blowing/suction on instability and transition control for a hypersonic flat plate boundary layer with Mach number 5.86 is investigated systematically. The influence of the blowing/suction flux and amplitude on instability is examined through direct numerical simulation and resolvent analysis. When a relatively small flux is used, the two-dimensional instability critical frequency that distinguishes the promotion/suppression mode effect closely aligns with the synchronisation frequency. For the oblique wave, as the spanwise wavenumber increases, the suppression effects would become weaker and the mode suppression bandwidth diminishes/increases in general in the blowing/suction control. Increasing the blowing/suction flux can effectively broaden the frequency bandwidth of disturbance suppression. The influence of amplitude on disturbance suppression is weak in a scenario of constant flux. To gain a deeper insight into disturbance suppression mechanism, momentum potential theory (MPT) and kinetic energy budget analysis are further employed in analysing disturbance evolution with and without control. When the disturbance is suppressed, the blowing induces the transport of certain acoustic components along the compression wave out of the boundary layer, whereas the suction does not. The velocity fluctuations are derived from the momentum fluctuations of the MPT. Compared with the momentum fluctuations, the evolutions indicated by each component's velocity fluctuations greatly facilitate the investigations of the acoustic nature of the second mode. The rapid variation of disturbance amplitude near the blowing is caused by the oscillations of the acoustic component and phase speed differences between vortical and thermal components. Kinetic energy budget analysis is performed to address the non-parallel effect of the boundary layer introduced by blowing/suction, which tends to suppress disturbances near the blowing. Moreover, viscous effects leading to energy dissipation are identified to be stronger in regions where the boundary layer is rapidly thickening. Finally, it is demonstrated that a flat plate boundary layer transition triggered by a random disturbance can be delayed by a blowing/suction combination control. The resolvent analysis further demonstrates that disturbances with frequencies that dominate the early transition stage are dampened in the controlled base flow.

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Effects of steps on the hypersonic boundary layer transition over a cone at 10° angle-of-attack

Han

et al. 2022

Physics of Fluids

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In a previous research on the hypersonic boundary layer transition over a sharp cone at 0° angle-of-attack ( AoA), we concluded the different effects of the forward-facing step (FFS) and the backward-facing step (BFS) on the transition [Xu et al., AIAA J. 59, 439–446 (2021)]. This further study intends to examine if the conclusion still maintains after changing the nose bluntness and the angle-of-attack of the cone. Experiments are conducted in a Mach 6 wind tunnel using nano-tracer-based planar laser scattering techniques, temperature sensitive paints, and high-frequency pressure sensors. The results show that although the FFS delays the boundary layer transition while the BFS promotes the transition at AoA = 0° and at AoA = 10°, a completely different pattern is observed; the FFS significantly promotes the transition, while the effect of the BFS appears only weakly to advocate the transition. Noteworthy, the nose bluntness will not change the effects of the BFS/FFS on the transition.

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Growth mechanisms of second-mode instability in hypersonic boundary layers

Abstract: Abstract

Cited by 10 publications

References 27 publications

A unified explanation of energy growth sources for unstable modes in flat-plate boundary layers

A unified explanation of energy growth sources for unstable modes in flat-plate boundary layers

Instability and transition control by steady local blowing/suction in a hypersonic boundary layer

Effects of steps on the hypersonic boundary layer transition over a cone at 10° angle-of-attack

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