A numerical evaluation of the asymptotic theory of receptivity for subsonic compressible boundary layers

Tullio, Nicola De; Ruban, Anatoly I.

doi:10.1017/jfm.2015.196

Cited by 20 publications

(28 citation statements)

References 42 publications

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“…At the same time, we know from a number of comparisons of the triple-deck theory with the Navier-Stokes simulations of the boundary-layer receptivity in subsonic flows that the triple-deck predictions are rather accurate (see e.g. Tumin 2006;Tullio & Ruban 2015). Therefore, we expect the results presented in this paper to be sufficiently accurate for engineering applications.…”

Section: Discussion Of the Resultsmentioning

confidence: 67%

Linear and nonlinear receptivity of the boundary layer in transonic flows

2015

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In this paper we analyse the process of the generation of Tollmien-Schlichting waves in a laminar boundary layer on an aircraft wing in the transonic flow regime. We assume that the boundary layer is exposed to a weak acoustic noise. As it penetrates the boundary layer, the Stokes layer forms on the wing surface. We further assume that the boundary layer encounters a local roughness on the wing surface in the form of a gap, step or hump. The interaction of the unsteady perturbations in the Stokes layer with steady perturbations produced by the wall roughness is shown to lead to the formation of the Tollmien-Schlichting wave behind the roughness. The ability of the flow in the boundary layer to convert 'external perturbations' into instability modes is termed the receptivity of the boundary layer. In this paper we first develop the linear receptivity theory. Assuming the Reynolds number to be large, we use the transonic version of the viscous-inviscid interaction theory that is known to describe the stability of the boundary layer on the lower branch of the neutral curve. The linear receptivity theory holds when the acoustic noise level is weak, and the roughness height is small. In this case we were able to deduce an analytic formula for the amplitude of the generated Tollmien-Schlichting wave. In the second part of the paper we lift the restriction on the roughness height, which allows us to study the flows with local separation regions. A new 'direct' numerical method has been developed for this purpose. We performed the calculations for different values of the Kármán-Guderley parameter, and found that the flow separation leads to a significant enhancement of the receptivity process.

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Section: Discussion Of the Resultsmentioning

confidence: 67%

Linear and nonlinear receptivity of the boundary layer in transonic flows

2015

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“…The parabolized stability equations 22,32,33 also partially capture non-parallel flow effects. 41 took on the acoustic receptivity problem by solving the compressible unsteady Navier-Stokes equations to compute the steady basic flows, and the LNS equations to obtain the unsteady perturbations. The vast majority of these works are computationally demanding, thus severely limiting their applicability in sensitivity and parametric investigations or design optimization analysis.…”

Section: Introductionmentioning

confidence: 99%

“…The reasons for pursuing this methodology are threefold: it is general and versatile enough to accommodate different receptivity mechanisms (vorticity, wing vibration, suction, heating) 17 , a wide range of flow conditions 41 , and finally non-linear corrections (both due to finite-height roughness and interaction of acoustic modes). It is sufficiently fast to be used recurrently (one acoustic frequency scenario can currently be computed in under 5 minutes approximately, using 20 CPU cores), while also enjoying the advantage of being able to calculate receptivity amplitudes for a range of different roughness shapes at little additional computational cost.…”

Section: Introductionmentioning

confidence: 99%

Acoustic receptivity and transition modeling of Tollmien-Schlichting disturbances induced by distributed surface roughness

2018

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Acoustic receptivity to Tollmien-Schlichting waves in the presence of surface roughness is investigated for a flat plate boundary layer using the time-harmonic incompressible linearized Navier-Stokes equations. It is shown to be an accurate and efficient means of predicting receptivity amplitudes, and therefore to be more suitable for parametric investigations than other approaches with DNS-like accuracy. Comparison with literature provides strong evidence of the correctness of the approach, including the ability to quantify non-parallel flow effects. These effects are found to be small for the efficiency function over a wide range of frequencies and local Reynolds numbers. In the presence of a two-dimensional wavy-wall, non-parallel flow effects are quite significant, producing both wavenumber detuning and an increase in maximum amplitude. However, a smaller influence is observed when considering an oblique Tollmien-Schlichting wave. This is explained by considering the non-parallel effects on receptivity and on linear growth which may, under certain conditions, cancel each other out. Ultimately, we undertake a Monte-Carlo type uncertainty quantification analysis with two-dimensional distributed random roughness. Its power spectral density (PSD) is assumed to follow a power law with an associated uncertainty following a probabilistic Gaussian distribution. The effects of the acoustic frequency over the mean amplitude of the generated two-dimensional Tollmien-Schlichting waves are studied. A strong dependence on the mean PSD shape is observed and discussed according to the basic resonance mechanisms leading to receptivity. The growth of Tollmien-Schlichting waves is predicted with non-linear parabolized stability equations computations to assess the effects of stochasticity in transition location.

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“…For example, comparisons with experiments (Wu 2001a, b) indicate that the theory, especially with the extension to second-order accuracy, predicts fairly accurately receptivity in the incompressible regime. Recent DNS studies (Mengaldo et al 2015, De Tullio & Ruban 2015 showed that the same is true for subsonic boundary layers. Nevertheless, further work is still needed in order to validate the present theoretical results for supersonic boundary layers.…”

Section: Discussionmentioning

confidence: 81%

Receptivity of supersonic boundary layers over smooth and wavy surfaces to impinging slow acoustic waves

Hernández

2019

J. Fluid Mech.

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In this paper, we investigate the receptivity of a supersonic boundary layer to impinging acoustic waves. Unlike previous studies of acoustic receptivity, where the sound waves have phase speeds comparable with or larger than the free-stream velocity $U_{\infty }$, the acoustic waves here have much slower ($O(R^{-1/8}U_{\infty })$) phase velocity, and their characteristic wavelength and frequency are of $O(R^{-3/8}L)$ and $O(R^{1/4}U_{\infty }/L)$ respectively, compatible with the triple-deck structure, where $L$ is the distance to the leading edge and $R$ the Reynolds number based on $L$ and $U_{\infty }$. A significant feature of a sound wave on the triple-deck scale is that an $O(\unicode[STIX]{x1D700}_{s})$ perturbation in the free stream generates much stronger ($O(\unicode[STIX]{x1D700}_{s}R^{1/8})$) velocity fluctuations in the boundary layer. Two receptivity mechanisms are considered. The first is new, involving the interaction of two such acoustic waves and operating in a boundary layer over a smooth wall. The second involves the interaction between an acoustic wave and the steady perturbation induced by a wavy wall. The sound–sound, or sound–roughness, interactions generate a forcing in resonance with a neutral Tollmien–Schlichting (T–S) wave. The latter is thus excited near the lower branch of the neutral curve, and subsequently undergoes exponential amplification. The excitation through sound–sound interaction may offer a possible explanation for the appearance of instability modes downstream of their neutral locations as was observed in a supersonic boundary layer over a smooth wall. The triple-deck formalism is adopted to describe impingement and reflection of the acoustic waves, and ensuing receptivity, allowing the coupling coefficient to be calculated. The two receptivity processes with the acoustic waves on the triple-deck scale are much more effective compared with those involving usual sound waves, with the coupling coefficient being greater by a factor of $O(R^{1/4})$ and $O(R^{1/8})$ in the sound–sound and sound–roughness interactions, respectively. A parametric study for both the reflection and coupling coefficients is conducted for representative T–S waves, to assess the influence of the streamwise and spanwise wavenumbers, and the phase speed (or frequency) of the acoustic wave.

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A numerical evaluation of the asymptotic theory of receptivity for subsonic compressible boundary layers

Cited by 20 publications

References 42 publications

Linear and nonlinear receptivity of the boundary layer in transonic flows

Linear and nonlinear receptivity of the boundary layer in transonic flows

Acoustic receptivity and transition modeling of Tollmien-Schlichting disturbances induced by distributed surface roughness

Receptivity of supersonic boundary layers over smooth and wavy surfaces to impinging slow acoustic waves

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