Boundary-layer receptivity to acoustic disturbances

Zhigulev, V. N.; Федоров, А. В.

doi:10.1007/bf00918768

Cited by 35 publications

(15 citation statements)

References 5 publications

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“…Despite the numerous efforts, comparisons between the predictions of the asymptotic theory of receptivity and the numerical and experimental results are very limited. Comparisons with experiments can be found for example in Goldstein & Hultgren (1987), Kozlov & Ryzhov (1990) and Wu (2001), while detailed comparisons with the predictions of the finite-Reynolds number Orr-Sommerfeld theory (Zhigulev & Fedorov 1987;Choudhari & Street 1992;Crouch 1992) are reported in Choudhari & Street (1992). However, the range of parameters over which the asymptotic theory has been compared with high-fidelity Navier-Stokes numerical simulations and/or experiments is very limited, hence a detailed evaluation of the capabilities of the theory is currently missing.…”

Section: Introductionmentioning

confidence: 99%

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

Tullio

Ruban

2015

J. Fluid Mech.

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The capabilities of the triple-deck theory of receptivity for subsonic compressible boundary layers have been thoroughly investigated through comparisons with numerical simulations of the compressible Navier-Stokes equations. The analysis focused on the two Tollmien-Schlichting wave linear receptivity problems arising due to the interaction between a low amplitude acoustic wave and a small isolated roughness element and the low amplitude, time-periodic vibrations of a ribbon placed on the wall of a flat plate. A parametric study was carried out to look at the effects of roughness element and vibrating ribbon longitudinal dimensions, Reynolds number, Mach number and TollmienSchlichting wave frequency. The flat plate is considered isothermal, with a temperature equal to the laminar adiabatic-wall temperature. Numerical simulations of the full and the linearised compressible Navier-Stokes equations have been carried out using highorder finite differences to obtain, respectively, the steady basic flows and the unsteady disturbance fields for the different flow configurations analysed. The results show that the asymptotic theory and the Navier-Stokes simulations are in good agreement. The initial Tollmien-Schlichting wave amplitudes and, in particular, the trends indicated by the theory across the whole parameter space are in excellent agreement with the numerical results. An important finding of the present study is that the behaviour of the theoretical solutions obtained for Re → ∞ holds at finite Reynolds numbers and the only conditions needed for the theoretical predictions to be accurate are that the receptivity process be linear and the free stream Mach number be subsonic.

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Section: Introductionmentioning

confidence: 99%

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

Tullio

Ruban

2015

J. Fluid Mech.

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“…In succeeding years, this approach led to the formulation of the biorthogonal eigenfunction system [36][37][38][39][40], which turned out to be a powerful technique in solving receptivity problems for spatially developing perturbations. The bulk of the results obtained with this approach were presented by Fedorov [41], including receptivity to acoustic waves interacting with a weakly nonparallel boundary layer [42], TS excitation by a local forcing [39][40], and receptivity to acoustic waves interacting with a wall waviness or a local roughness element [43] (see also [44]). However, the aforementioned results at finite Reynolds numbers were prone to uncertainty in the path of integration in the inverse Fourier transform at supercritical frequencies of the forcing.…”

Section: Introductionmentioning

confidence: 99%

Biorthogonal Eigenfunction System in the Triple‐Deck Limit

Tumin

2006

Stud Appl Math

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The solutions of receptivity problems for a periodic-in-time actuator placed on the wall in a two-dimensional boundary layer and for a two-dimensional hump are discussed within the scope of the biorthogonal eigenfunction expansion technique in the limit of high Reynolds number when the triple-deck scaling is imposed. It is shown that the solutions obtained with the help of the biorthogonal eigenfunction system are equivalent to the solutions derived within the scope of the triple-deck theory.

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“…Adjoint methods have recently been used to predict the receptivity characteristics of a wide range of flows including pipe Poiseuille flow, 15 the Blasius boundary layer, 9,12,18 laminar wall jets, 17 and Görtler vortices in boundary layers on concave surfaces. 11 With the exception of the work of Luchini & Bottaro, 11 all of these studies rely on the expansion of the homogeneous solution to the locally parallel flow into a biorthogonal set of eigenfunctions as described by Salwen & Grosch.…”

Section: Introductionmentioning

confidence: 99%

Adjoint parabolized stability equations for receptivity prediction

Dobrinsky

Collis

2000

Fluids 2000 Conference and Exhibit

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This paper presents the Adjoint Parabolized Stability Equations (APSE) which are used to predict the receptivity of shear layers to a variety of disturbances. Results from the APSE are first carefully validated against solutions of the Adjoint Navier-Stokes (ANS) equations which demonstrates that APSE is an accurate and effecient means of predicting receptivity. Then APSE is used to document the nonparallel receptivity characteristics of both Blasius and Falkner-Skan boundary layers for two-dimensional and oblique Tollmein-Schlichting (TS) instabilities. These results are compared to receptivity predictions based on local parallel theory in order to establish the effects of mean boundary layer growth on receptivity. In general, the inclusion of nonparallel effects for the receptivity prediction of TS instabilities is found to be small under all conditions. Comparing results from Blasius and Falkner-Skan base flows shows that adverse pressure gradients tend to reduce receptivity while favorable pressure gradients lead to an increase in receptivity. This is in contrast to the well known effects of pressure gradient on TS instability growth rates. Likewise, our investigations for three-dimensional disturbances also show that oblique modes have greater receptivity than two dimensional waves, again in contrast to the effects of obliquity on instability growth rates. In general there is a trade-off between receptivity and instability -the stronger the instability the weaker the receptivity.

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Boundary-layer receptivity to acoustic disturbances

Cited by 35 publications

References 5 publications

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

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

Biorthogonal Eigenfunction System in the Triple‐Deck Limit

Adjoint parabolized stability equations for receptivity prediction

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