From primary instabilities to secondary instabilities in Görtler vortex flows

Chen, Xi; Chen, Jianqiang; Yuan, Xianxu; Tu, Guohua; Zhang, Yifeng

doi:10.1186/s42774-019-0021-8

Cited by 17 publications

(4 citation statements)

References 29 publications

(35 reference statements)

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“…Since the growth rate increases rapidly near the neutral location, the uncertainty of N-factors due to the neutral location is much smaller than the difference caused by different inlet modes, and is thus acceptable. The code has been well validated in previous studies (Chen et al 2019a(Chen et al , 2020Chen, Huang & Lee 2019b). Grid convergence relative to the grid was assessed via spot checks for different types of instabilities.…”

Section: Biglobal Methodsmentioning

confidence: 99%

“…As a result, accurately tracking a single mode in the axial direction is nearly impossible and also of insignificance in practice. In comparison, PSE3D is able to capture adequately evolution of instabilities in the context of multiple modes (Chen et al 2019a;Choudhari et al 2020), and turns out to be less sensitive to the grid resolution, as shown in Appendix E. Therefore, we utilize PSE3D to follow evolutions of cross-flow instabilities in this paper. Figure 27(a,b) show the evolution of N-factors and phase velocities obtained by PSE3D with frequency 30 kHz but different initial conditions, say different inlet modes or different inlet locations.…”

Section: Shoulder Cross-flow Regionmentioning

confidence: 99%

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Boundary layer transition and linear modal instabilities of hypersonic flow over a lifting body

Chen

Dong

et al. 2022

J. Fluid Mech.

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Boundary layer transition over a lifting body of 1.6 m length at $2^\circ$ angle of attack has been simulated at Mach 6 and a unit Reynolds number $1.0 \times 10^7$ m $^{-1}$ . The model geometry is the same as the Hypersonic Transition Research Vehicle designed by the China Aerodynamics Research and Development Center. Four distinct transitional regions are identified, i.e. windward vortex region, shoulder vortex region, windward cross-flow region and shoulder cross-flow region. Multi-dimensional linear stability analyses by solving the two-dimensional eigenvalue problem (spatial BiGlobal approach) and the plane-marching parabolized stability equations (PSE3D approach) are further carried out to uncover the dominant instabilities in the last three regions as well as the shoulder attachment-line region. The shoulder vortex is conducive to both inner and outer modes of shear-layer instability, of which the latter most likely trigger the vortex breakdown. A novel method is presented to substantially reduce the computational cost of BiGlobal and PSE3D in resolving the cross-flow instabilities in cross-flow regions. The peak frequencies of cross-flow modes lie between 15 and 45 kHz. Whereas oblique second Mack modes are marginally unstable in the windward cross-flow region, they could be strong enough to compete with the cross-flow modes in the shoulder cross-flow region. In the shoulder attachment-line region, there exists only one unstable mode of Mack instability, differing from previous studies that show a hierarchy of modes in the context of symmetrical attachment-line flows. Results of the numerical simulation and multi-dimensional stability analyses are compared when possible, showing a fair agreement between the two approaches and highlighting the necessity of considering non-parallel effects.

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Section: Biglobal Methodsmentioning

confidence: 99%

Section: Shoulder Cross-flow Regionmentioning

confidence: 99%

Boundary layer transition and linear modal instabilities of hypersonic flow over a lifting body

Chen

Dong

et al. 2022

J. Fluid Mech.

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“…Questions on the secondary Görtler instability of compressible ŕows remain open, such as the receptivity of nonlinearly saturated compressible vortices, leading to the excitation of secondary-instability modes. By comparing the two-dimensional linear-stability results with the biglobal results for a Mach 6.5 boundary layer over a planar concave wall, Chen et al [112] indicated that the second Mack mode can become a secondary varicose mode, whereas the őrst Mack mode can develop into either a secondary instability sinuous mode or a secondary instability varicose mode, depending on its frequency and spanwise wavelength (refer also to Chen et al [116]). Figure 5, adapted from őgure 14 of Chen et al [112], reveals the similarity of a secondary varicose mode with a Mack mode.…”

Section: E Secondary Instabilitymentioning

confidence: 99%

“…Chen et al [112,116] and Song et al [87] investigated the secondary instability and breakdown of stationary Görtler vortices in a Mach 6.5 boundary layer over a planar concave wall by performing DNS. Their DNS results were compared with results from biglobal stability analyses and PSE calculations.…”

Section: A Flows Over Spanwise-planar Concave Wallsmentioning

confidence: 99%

Görtler Instability and Transition in Compressible Flows

Xu,

Ricco,

Duan

2024

AIAA Journal

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We present a discussion on theoretical, experimental, and computational research studies on Görtler instability and the related transition to turbulence occurring in compressible boundary layers over concave surfaces. We first examine the theoretical results on primary and secondary instabilities, emphasizing the role of receptivity, the mechanism by which external agents, such as freestream fluctuations or wall roughness, act on a boundary layer to trigger Görtler vortices. We review experimental findings obtained from measurements in supersonic and hypersonic wind tunnels and discuss studies employing numerical methods, focusing on the direct numerical simulation approach. The research in these two last sections is surveyed according to the geometrical configuration, from simple concave walls to more complex surfaces of hypersonic vehicles. The experimental investigations have been successful in the visualizations of Görtler vortices, in the measurement of the wall-heat transfer in the transitional region, and in the computation of the Görtler-vortex growth rates, although detailed boundary-layer velocity measurements are still missing. Direct numerical simulations have confirmed instability results emerging from stability theories and revealed nonlinear interactions between Görtler vortices and other disturbances. The established initial-boundary-value receptivity theory can certainly benefit from more advanced experimental measurements, and receptivity results should be used in combination with direct numerical simulations. A major conclusion of our review is therefore that the understanding of Görtler vortices should be pursued by a combined methodology including theoretical analysis based on the receptivity formalism, direct numerical simulation, and experiments. Highly desirable outcomes of such endeavor are the prediction of the location and extension of the transition region, and a model for the transition process. We finally highlight further prospects and challenges on fundamental and applied research on Görtler instability and transition in compressible flows.

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Effects of nose bluntness on entropy-layer stabilities over cones and wedges

Wan

Chen

et al. 2022

Acta Mech. Sin.

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From primary instabilities to secondary instabilities in Görtler vortex flows

Cited by 17 publications

References 29 publications

Boundary layer transition and linear modal instabilities of hypersonic flow over a lifting body

Boundary layer transition and linear modal instabilities of hypersonic flow over a lifting body

Görtler Instability and Transition in Compressible Flows

Effects of nose bluntness on entropy-layer stabilities over cones and wedges

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