6 results
Receptivity of inviscid modes in supersonic boundary layers due to scattering of free-stream sound by localised wall roughness
- Ming Dong, Yinhui Liu, Xuesong Wu
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- Journal:
- Journal of Fluid Mechanics / Volume 896 / 10 August 2020
- Published online by Cambridge University Press:
- 04 June 2020, A23
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The present paper investigates the receptivity of inviscid first and second modes in super/hypersonic boundary layers due to the interaction between a weak free-stream acoustic wave and a small isolated surface roughness element. The large-Reynolds-number asymptotic analysis reveals the detailed processes of the excitation. The distortion of the acoustic signature by the curved wall contributes to the leading-order receptivity, producing an eigenmode of $O({\mathcal{E}}h)$ amplitude, where ${\mathcal{E}}\ll 1$ is the magnitude of the acoustic wave and $h\ll 1$ the roughness height normalised by the local boundary-layer thickness $\unicode[STIX]{x1D6FF}$. The interactions between the roughness-induced mean-flow distortion and the acoustic signature contribute to the second-order receptivity, which is of $O({\mathcal{E}}hR^{-1/3})$ with $R\gg 1$ being the Reynolds number based on $\unicode[STIX]{x1D6FF}$. Interestingly, the leading-order receptivity is equivalent to a canonic receptivity problem, the excitation by time-periodic blowing and suction through a local slot on the wall, and the effective periodic outflux velocity forced from the underneath Stokes layer can be determined explicitly in terms of the roughness shape function. This equivalence holds when $h=O(R^{-1/3})$, for which the roughness-induced mean-flow distortion becomes nonlinear. A systematic parametric study is carried out for the excitation of the first and second modes by both fast and slow free-stream acoustic waves, and the dependence of the receptivity efficiency on the relevant parameters is provided. Interestingly, the second-order receptivity could become dominant (e.g. in the case of slow acoustic waves with low frequencies and small incident angles), but the present mathematical theory remains valid. In order to check the accuracy of the asymptotic predictions, we have carried out direct numerical simulations (DNS) and also extended the existing finite-Reynolds-number theory to the supersonic regime. The asymptotic solutions agree with the results given by the finite-Reynolds-number calculations and DNS when $R$ is sufficiently large (typically $R=O(10^{5})$). An improved large-Reynolds-number approach is developed by replacing the non-penetration boundary condition by an unsteady outflux, which accounts for the $O(R^{-1/2})$ viscous correction by the Stokes layer. With this modification, the accuracy of the receptivity calculation at moderate Reynolds numbers (approximately a few thousands) is improved remarkably.
Generation of first Mack modes in supersonic boundary layers by slow acoustic waves interacting with streamwise isolated wall roughness
- Yinhui Liu, Ming Dong, Xuesong Wu
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- Journal:
- Journal of Fluid Mechanics / Volume 888 / 10 April 2020
- Published online by Cambridge University Press:
- 06 February 2020, A10
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This paper investigates the receptivity of a supersonic boundary layer to slow acoustic waves whose characteristic frequency and wavelength are on the triple-deck scales, and the phase speed is thus asymptotically small. Acoustic waves on these scales are of special importance as they have the interesting property that a perturbation with a magnitude of $O(\unicode[STIX]{x1D716}_{u})$ in the free stream generates much larger, $O(\unicode[STIX]{x1D700}_{u}R^{1/8})$, velocity fluctuations inside the boundary layer, where $R$ is the Reynolds number based on the distance to the leading edge. Their interaction with streamwise localized roughness elements, leading to stronger receptivity, is studied using triple-deck theory and direct numerical simulations (DNS). The receptivity coefficient, defined as the ratio of the streamwise-velocity amplitude of the instability mode excited to that of the incident free-stream acoustic wave, serves to characterize receptivity efficiency. Its dependence on the roughness width, the Reynolds number $R$, the free-stream Mach number $M$ and the incident angle of the acoustic wave is examined. The theoretical predictions, obtained assuming $R\gg 1$, are found to be in quantitative agreement with the DNS results at moderate values of $R$ when the roughness elements are located near the lower branch of the instability. The receptivity is sensitive to the incident angle (or the phase speed) of the acoustic wave, being highly effective within a small range of angles close to $\cos ^{-1}(1/M)$ and $\unicode[STIX]{x03C0}+\cos ^{-1}(1/M)$ for downstream and upstream propagating sound waves, respectively. The amplitude of the instability mode excited is proportional to the streamwise-velocity amplitude of the acoustic signature inside the boundary layer, and scales with the roughness height $h^{\ast }$ as $(h^{\ast }/\unicode[STIX]{x1D6FF}^{\ast })R^{1/4}$, where $\unicode[STIX]{x1D6FF}^{\ast }$ is the boundary-layer thickness.
Entrainment of short-wavelength free-stream vortical disturbances in compressible and incompressible boundary layers
- Xuesong Wu, Ming Dong
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- Journal:
- Journal of Fluid Mechanics / Volume 797 / 25 June 2016
- Published online by Cambridge University Press:
- 24 May 2016, pp. 683-728
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The fundamental difference between continuous modes of the Orr–Sommerfeld/Squire equations and the entrainment of free-stream vortical disturbances (FSVD) into the boundary layer has been investigated in a recent paper (Dong & Wu, J. Fluid Mech., vol. 732, 2013, pp. 616–659). It was shown there that the non-parallel-flow effect plays a leading-order role in the entrainment, and neglecting it at the outset, as is done in the continuous-mode formulation, leads to non-physical features of ‘Fourier entanglement’ and abnormal anisotropy. The analysis, which was for incompressible boundary layers and for FSVD with a characteristic wavelength of the order of the local boundary-layer thickness, is extended in this paper to compressible boundary layers and FSVD with even shorter wavelengths, which are comparable with the width of the so-called edge layer. Non-parallelism remains a leading-order effect in the present scaling, which turns out to be more general in that the equations and solutions in the previous paper are recovered in the appropriate limit. Appropriate asymptotic solutions in the main and edge layers are obtained to characterize the entrainment. It is found that when the Prandtl number $\mathit{Pr}<1$, free-stream vortical disturbances of relatively low frequency generate very strong temperature fluctuations within the edge layer, leading to formation of thermal streaks. A composite solution, uniformly valid across the entire boundary layer, is constructed, and it can be used in receptivity studies and as inlet conditions for direct numerical simulations of bypass transition. For compressible boundary layers, continuous spectra of the disturbance equations linearized about a parallel base flow exhibit entanglement between vortical and entropy modes, namely, a vortical mode necessarily induces an entropy disturbance in the free stream and vice versa, and this amounts to a further non-physical behaviour. High Reynolds number asymptotic analysis yields the relations between the amplitudes of entangled modes.
A local scattering theory for the effects of isolated roughness on boundary-layer instability and transition: transmission coefficient as an eigenvalue
- Xuesong Wu, Ming Dong
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- Journal:
- Journal of Fluid Mechanics / Volume 794 / 10 May 2016
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- 30 March 2016, pp. 68-108
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This paper is concerned with the rather broad issue of the impact of abrupt changes (such as isolated roughness, gaps and local suctions) on boundary-layer transition. To fix the idea, we consider the influence of a two-dimensional localized hump (or indentation) on an oncoming Tollmien–Schlichting (T–S) wave. We show that when the length scale of the former is comparable with the characteristic wavelength of the latter, the key physical mechanism to affect transition is through scattering of T–S waves by the roughness-induced mean-flow distortion. An appropriate mathematical theory, consisting of the boundary-value problem governing the local scattering, is formulated based on triple deck formalism. The transmission coefficient, defined as the ratio of the amplitude of the T–S wave downstream of the roughness to that upstream, serves to characterize the impact on transition. The transmission coefficient appears as the eigenvalue of the discretized boundary-value problem. The latter is solved numerically, and the dependence of the eigenvalue on the height and width of the roughness and the frequency of the T–S wave is investigated. For a roughness element without causing separation, the transmission coefficient is found to be approximately 1.5 for typical frequencies, indicating a moderate but appreciable destabilizing effect. For a roughness causing incipient separation, the transmission coefficient can be as large as $O(10)$, suggesting that immediate transition may take place at the roughness site. A roughness element with a fixed height produces the strongest impact when its width is comparable with the T–S wavelength, in which case the traditional linear stability theory is invalid. The latter however holds approximately when the roughness width is sufficiently large. By studying the two hump case, a criterion when two roughness elements can be regarded as being isolated is suggested. The transmission coefficient can be converted to an equivalent $N$-factor increment, by making use of which the $\text{e}^{N}$-method can be extended to predict transition in the presence of multiple roughness elements.
Association of unipolar depression with gene polymorphisms in the serotonergic pathways in Han Chinese
- Mei Shi, Jian Hu, Xuesong Dong, Yue Gao, Ganghui An, Wei Liu, Li Chen, Xueying Sun
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- Journal:
- Acta Neuropsychiatrica / Volume 20 / Issue 3 / June 2008
- Published online by Cambridge University Press:
- 24 June 2014, pp. 139-144
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Objective:
The present study aims to investigate the association of unipolar depression (UPD) with six serotonergic gene polymorphisms in Han Chinese.
Methods:One hundred and thirty-two UPD patients and 180 healthy controls were genotyped for polymorphisms of six serotonergic genes, including tryptophan hydroxylase (TPH1 A218C), serotonin transporter promoter region (5-HTTLPR), serotonin receptor 2A (5-HT2AR −1438G/A), serotonin receptor 2C (5-HT2CR Cys23Ser), serotonin receptor 6 (5-HT6R C267T) and serotonin receptor 1Dβ (5-HT1DβR T371G). Symptomatic clusters were evaluated by the 24-item Hamilton Rating Scale for Depression (HAMD).
Results:The frequencies of S/S genotype and S allele in 5-HTTLPR polymorphism were significantly higher in UPD patients than in healthy controls. There was a significant difference in distributions of genotypes in 5-HT2CR Cys23Ser polymorphism between UPD patients and control subjects, but the difference became no significant when the data were further stratified by gender. The patients with genotypes G/G and T/G of 5-HT1DβR T371G polymorphism had significantly lower scores of diurnal variation evaluated by HAMD than those with genotype T/T, while the patients with genotype T/G had significantly higher scores of hopelessness than those with genotypes G/G and T/T. There were no significant differences in genotypic and allelic distributions of TPH1 A218C, 5-HT2AR −1438G/A or 5-HT6R C267T polymorphisms between the case and control groups.
Conclusion:The study demonstrates that 5-HTTLPR and 5-HT2CR Cys23Ser polymorphisms might contribute to susceptibility of UPD, and the genotype T/T in 5-HT1DβR T371G polymorphism might be a risk factor for diurnal variation, while T/G might be a protective factor against hopelessness in Han Chinese populations.
On continuous spectra of the Orr–Sommerfeld/Squire equations and entrainment of free-stream vortical disturbances
- Ming Dong, Xuesong Wu
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- Journal:
- Journal of Fluid Mechanics / Volume 732 / 10 October 2013
- Published online by Cambridge University Press:
- 12 September 2013, pp. 616-659
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Small-amplitude perturbations are governed by the linearized Navier–Stokes equations, which are, for a parallel or nearly parallel shear flow, customarily reduced to the Orr–Sommerfeld (O-S) and Squire equations. In this paper, we consider continuous spectra (CS) of the O-S and Squire operators for the Blasius and asymptotic suction boundary layers, and address the issue of whether and when continuous modes can represent free-stream vortical disturbances and their entrainment into the shear layer. For the Blasius boundary layer, we highlight two particular properties of the CS: (i) the eigenfunction of a continuous mode simultaneously consists of two components with wall-normal wavenumbers $\pm {k}_{2} $, a phenomenon which we refer to as ‘entanglement of Fourier components’; and (ii) for low-frequency disturbances the presence of the boundary layer forces the streamwise velocity in the free stream to take a much larger amplitude than those of the transverse velocities. Both features appear to be non-physical, and cast some doubt about the appropriateness of using CS to characterize free-stream vortical disturbances and their entrainment into the boundary layer, a practice that has been adopted in some recent studies of bypass transition. A high-Reynolds-number asymptotic description of continuous modes and entrainment is present, and it shows that the entanglement is a result of neglecting non-parallelism, which has a leading-order effect on the entrainment. When this effect is included, entanglement disappears, and moreover the streamwise velocity is significantly amplified in the edge layer when ${R}^{- 1} \ll \omega \ll 1$, where $R$ is the Reynolds number based on the local boundary-layer thickness. For the asymptotic suction boundary layer, which is an exactly parallel flow, both temporal and spatial CS may be defined mathematically. However, at a finite $R$ neither of them represents the physical process of free-stream vortical disturbances penetrating into the boundary layer. The latter must instead be characterized by a peculiar type of continuous modes whose eigenfunctions increase exponentially with the distance from the wall. In the limit $R\gg 1$, all three types of CS are identical at leading order, and hence can be used to represent free-stream vortical disturbances and their entrainment. Low-frequency disturbances are found to generate a large-amplitude streamwise velocity in the boundary layer, which is reminiscent of longitudinal streaks.