Improvement for expansion of parabolized stability equation method in boundary layer stability analysis

Luo, Juan; Han, Ya Fang; Liu, Jianxin

doi:10.1007/s10483-019-2401-9

Appl. Math. Mech.-Engl. Ed.

2018

DOI: 10.1007/s10483-019-2401-9

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Improvement for expansion of parabolized stability equation method in boundary layer stability analysis

Juan Luo

Ya Fang Han

Jianxin Liu

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Cited by 2 publications

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Three-dimensional wall heating elements effect on the instability in zero pressure gradient supersonic boundary layers

Wang

et al. 2023

Physics of Fluids

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The streaky boundary layers have very important roles in laminar-turbulent transition. Streaks of appropriate size can influence stabilities in boundary layers. In this paper, the effect of streamwise-elongated, spanwise periodic wall heating elements on the first mode instability in supersonic flat plate boundary layers was investigated. For the balance of the efficient and accuracy, the Linearized Navier-Stokes Equations (LNSE) is used to obtain the base flow and compared with compressible Navier-Stokes equations. A biglobal analysis tool is used for the instability analysis because the heating source has a much larger length-scale in the streamwise direction than that in the spanwise direction and the streamwise velocity is much larger than the normal velocity and the spanwise one. Results indicated that the distortion caused by the three-dimensional surface heating elements could modify the first mode, resulting in a lower frequency but with an uncertain effect on the higher frequency modes. Additionally, the streaks make the lower spanwise wave number components of the even first mode disturbance in a three dimensional supersonic boundary layer in the free-stream. As a result, the spontaneous radiation of an acoustic wave to the far field was found for the even mode. These findings suggest that laminar-turbulence transition can be suppressed or enhanced by the three-dimensional wall heating.

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Three-dimensional wall heating elements effect on the instability in zero pressure gradient supersonic boundary layers

Wang

et al. 2023

Physics of Fluids

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Effects of streak structure in oblique resonance on the instability in supersonic plate boundary layers

Li,

Huang,

Liu

2024

Physics of Fluids

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Streaks are large-scale coherent structures in flows and play an important role in the laminar–turbulent transition. In this paper, the effect of streaks in oblique resonance on the instabilities of the first mode with the same spanwise wavenumber as the streaks is investigated. The streaks are obtained by the nonlinear parabolized stability equations, and the instability is analyzed by the bi-global analysis tool. Streaks can be decomposed into the two-dimensional mean-flow distortion (MFD) and the three-dimensional streak modes (SMs). For odd modes, the effects of the MFD dominate, stabilizing low-frequency waves and destabilizing high-frequency waves at small streak amplitudes. While the opposite effects of the SMs dominate at large streak amplitudes. Even modes show similar responses, except for the stabilization of low-frequency waves. The results of the global energy balance indicate that the more negative work of pressure-dilatation terms is responsible for the stabilization of the high-frequency waves compared to low-frequency waves at large streak amplitudes. Due to the stronger concentration of streamwise velocity distribution and the more negative Reynolds stress work in the spanwise direction, the even modes are more stabilized compared to the odd modes. Additionally, streaks can modify the distribution of the Fourier components of the even mode pressure in the spanwise direction; thus, they can induce the spontaneous excitation of a radiating component to the far field.

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Improvement for expansion of parabolized stability equation method in boundary layer stability analysis

Cited by 2 publications

References 10 publications

Three-dimensional wall heating elements effect on the instability in zero pressure gradient supersonic boundary layers

Three-dimensional wall heating elements effect on the instability in zero pressure gradient supersonic boundary layers

Effects of streak structure in oblique resonance on the instability in supersonic plate boundary layers

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