Trapped waves in supersonic and hypersonic turbulent channel flow over porous walls

Chen, Yongkai; Scalo, Carlo

doi:10.1017/jfm.2021.428

Cited by 15 publications

(12 citation statements)

References 60 publications

(128 reference statements)

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“…These models have been applied to compressible turbulence, and some of them were applied to the hypersonic regime (Bhagwandin & Martin 2021;Chen & Scalo 2021b;Helm 2021;Helm & Martin 2022;Camillo et al 2023). On the other hand, discussions about the SFS terms in hypersonic wall-bounded flows are very limited although there are several DNS studies (Martin 2007;Li, Fu & Ma 2008;Duan, Beekman & Martin 2011;Franko & Lele 2013;Zhang, Duan & Choudhari 2018;Chen & Scalo 2021b;Helm 2021;Xu et al 2021a,b;Chen et al 2022;Huang, Duan & Choudhari 2022;Xu, Wang & Chen 2022). To the best of the authors' knowledge, there are only two studies that investigated the SFS terms using DNS of hypersonic wall-bounded flows.…”

Section: Extension To Compressible Turbulencementioning

confidence: 99%

“…In compressible wall-bounded flows the semi-local Reynolds number , rather, dictates the characteristic size of the near-wall structures. In fact, increasing the Mach number while keeping constant (see Chen & Scalo 2021 b ) results in an increase of the friction Reynolds number . However, the resulting increase of values does not indicate a degradation of the grid resolution since the size of the turbulent structures scales with semi-local units, which read .…”

Section: Configuration and Conditionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…2023). On the other hand, discussions about the SFS terms in hypersonic wall-bounded flows are very limited although there are several DNS studies (Martin 2007; Li, Fu & Ma 2008; Duan, Beekman & Martin 2011; Duan & Martin 2011; Franko & Lele 2013; Zhang, Duan & Choudhari 2018; Chen & Scalo 2021 b ; Helm 2021; Xu et al. 2021 a , b ; Chen et al.…”

Section: Introductionmentioning

confidence: 99%

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Sub-filter-scale shear stress analysis in hypersonic turbulent Couette flow

Toki,

Sousa,

Chen

et al. 2024

J. Fluid Mech.

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Direct numerical simulations of hypersonic turbulent Couette flows are performed for top-wall Mach numbers of 6, 7 and 8, inspired by non-reactive high-enthalpy wind tunnel free-stream conditions, with the goal of analysing the physical processes driving the sub-filter-scale (SFS) stresses to inform development of large-eddy simulation techniques for hypersonic wall-bounded flows. Semi-local scaling laws collapse mean profiles and second-order turbulent statistics well, in spite of the strong wall-normal gradients of temperature and density. On the other hand, the SFS shear stresses exhibit an unexpected profile characterized by a region of pronounced shear stress deficit, which becomes more pronounced for higher Mach numbers. Instantaneous visualizations suggest that the SFS shear stress deficit is induced by the counter-gradient resolved momentum transport driven by residual velocity motions at the interface between high-density low-speed streaks being ejected away from the wall, and low-density high-speed ones replacing the displaced fluid, qualifying this as a compressibility effect. It is shown that the SFS shear stresses are primarily driven by second-order interactions between residual velocities, in spite of their triply nonlinear nature. This, in turn, motivated a statistical quadrant analysis revealing the presence of a SFS shear stress deficit, that is, SFS processes driving momentum transport of the resolved field towards the top wall. Additionally, higher-Reynolds-number simulations reveal that there is an upper limit of spatial filter widths to resolve large-scale structures, and such deficit is observable at any Reynolds number when a reasonable spatial filter is applied.

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Section: Extension To Compressible Turbulencementioning

confidence: 99%

Section: Configuration and Conditionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Sub-filter-scale shear stress analysis in hypersonic turbulent Couette flow

Toki,

Sousa,

Chen

et al. 2024

J. Fluid Mech.

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“…If the thickness and tension of the membrane are zero, i.e. a = b = 0, then the admittance condition recovers to that of the porous wall, so the porous-wall admittance is K. The admittance sometimes also appears as an impedance, which is the reciprocal of the former (Scalo, Bodart & Lele 2015;Chen & Scalo 2021). At first glance, we may find that the denominator of A shares the same form as the Helmholtz resonator impedance model as in Tam & Auriault (1996), but there are certain differences.…”

Section: Model Of the Admittance Boundary Condition On The Compliant ...mentioning

confidence: 99%

Impact of compliant coating on Mack-mode evolution in hypersonic boundary layers

Ji,

Dong,

Zhao

2023

J. Fluid Mech.

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This paper focuses on the linear evolution of Mack instability modes in a hypersonic boundary layer over a flat plate that is partially coated by a compliant section. The compliant section is a thin, flexible membrane covering on a porous wall consisting of micro holes. The instability pressure could induce a vibration of the membrane, leading to a feedback to the boundary-layer fluids through the transverse velocity fluctuation. Such a process is formulated by an admittance boundary condition for the boundary-layer perturbation, which is dependent on the thickness and tension of the membrane, the properties of the porous wall, and the frequency of the Mack-mode perturbation. Using this admittance condition, the impact of the compliant coating on the Mack growth rate is studied systematically by solving the compressible Orr–Sommerfeld equations. It is found that the compliant coating could suppress the Mack instability with a frequency band in the neighbourhood of the most unstable frequency, and the stabilising frequency band widens as the membrane thickness and tension decrease, indicating a more favourable effect of a softer membrane. For a Mack mode with a specified dimensional frequency – since its dimensionless frequency, normalised by the local boundary-layer thickness and oncoming velocity, increases as it propagates downstream – the second-mode frequency band usually appears in downstream locations, and so does the stabilising effect of the membrane. Thus it is favourable to apply a compliant panel at a downstream region. In this situation, the solid–compliant junction could produce an additional scattering effect on the evolution of the Mack mode due to the sudden change of its boundary condition. The scattering effect is quantified by a transmission coefficient defined by the equivalent amplitude of the compliant-wall perturbation to the solid-wall perturbation, which can be obtained by the harmonic linearised Navier–Stokes (HLNS) approach. If the admittance is weak, then the transmission coefficient can also be predicted by an analytical solution based on the residue theorem. It is found that most of the second modes are suppressed by the scattering effect as long as the argument of the admittance is in the interval $[150^\circ, 210^\circ ]$ , agreeing with most of the physical situation. The analytical predictions agree well with the HLNS calculations when the modulus of the admittance is less than $O(0.1)$ .

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