Scattering of acoustic waves into Tollmien-Schlichting waves by small streamwise variations in surface geometry

1985 ◽  
Vol 154 ◽  
pp. 509-529 ◽  
Author(s):  
M. E. Goldstein
Keyword(s):  
Boundary Layer ◽  
Acoustic Waves ◽  
Static Pressure ◽  
Quantitative Agreement ◽  
Qualitative Explanation ◽  
Surface Geometry ◽  
Acoustic Disturbance ◽  
Good Quantitative Agreement ◽  
Tollmien Schlichting ◽  
Scattering Of Acoustic Waves

By using the triple-deck scaling of Stewartson (1969) and Messiter (1970) we show that small but relatively sudden surface geometry variations that produce only very weak static pressure variations can nevertheless produce strong, i.e. 0(1), coupling between an externally imposed acoustic disturbance and a spatially growing Tollmien- Schlichting wave. The analysis provides a qualitative explanation of the Leehey & Shapiro (1979) boundary-layer receptivity measurements and is in good quantitative agreement with the Aizin & Polyakov (1979) experiment. It may also explain why small ‘trip wires’ can promote early transition.

Leading-edge receptivity of a hypersonic boundary layer on a flat plate

2001 ◽  
Vol 426 ◽  
pp. 73-94 ◽  
Author(s):  
A. A. MASLOV ◽  
A. N. SHIPLYUK ◽  
A. A. SIDORENKO ◽  
D. ARNAL
Keyword(s):  
Boundary Layer ◽  
Acoustic Waves ◽  
Free Stream ◽  
Three Dimensional ◽  
Leading Edge ◽  
Experimental Investigations ◽  
Two Dimensional ◽  
Inclination Angles ◽  
Tollmien Schlichting ◽  
Radiation Conditions

Experimental investigations of the boundary layer receptivity, on the sharp leading edge of a at plate, to acoustic waves induced by two-dimensional and three- dimensional perturbers, have been performed for a free-stream Mach number M∞ = 5.92. The fields of controlled free-stream disturbances were studied. It was shown that two-dimensional and three-dimensional perturbers radiate acoustic waves and that these perturbers present a set of harmonic motionless sources and moving sources with constant amplitude. The disturbances excited in the boundary layer were measured. It was found that acoustic waves impinging on the leading edge generate Tollmien–Schlichting waves in the boundary layer. The receptivity coefficients were obtained for several radiation conditions and intensities. It was shown that there is a dependence of receptivity coefficients on the wave inclination angles.

On the Generation of Instability Tollmien-Schlichting Waves by Free-Stream Turbulence

2017 ◽  
Vol 9 (2) ◽  
pp. 429-438
Author(s):  
Luyu Shen ◽  
Changgen Lu
Keyword(s):  
Boundary Layer ◽  
Acoustic Waves ◽  
Free Stream ◽  
Leading Edge ◽  
S Wave ◽  
S Waves ◽  
Free Stream Turbulence ◽  
Temporal Mode ◽  
Tollmien Schlichting ◽  
Experimental Researches

AbstractThe beginning of the transition from the laminar to a turbulent flow is usually the generation of instability Tollmien-Schlichting (T-S) waves in the boundary layer. Previously, most numerical and experimental researches focused on generating instability T-S waves through the external disturbances such as acoustic waves and vortical disturbances interacting with wall roughness or at the leading-edge of flatplate, whereas only a few paid attention to the excitation of the T-S waves directly by free-stream turbulence (FST). In this study, the generating mechanism of the temporal mode T-S waves under free-stream turbulence is investigated by using direct numerical simulation (DNS) and fast Fourier transform. Wave packets superposed by a group of stability, neutral and instability T-S waves are discovered in the boundary layer. In addition, the relation between the amplitude of the imposed free-stream turbulence and the amplitude of the excited T-S wave is also obtained.

Nonlinear Triple-Deck Studies in Boundary-Layer Receptivity

1990 ◽  
Vol 43 (5S) ◽  
pp. S158-S166 ◽  
Author(s):  
R. J. Bodonyi
Keyword(s):  
Boundary Layer ◽  
Finite Difference ◽  
Steady Flow ◽  
Strouhal Number ◽  
Spectral Methods ◽  
Numerical Solutions ◽  
Free Stream ◽  
Numerical Study ◽  
Surface Geometry ◽  
Tollmien Schlichting

A numerical study of the generation of Tollmien-Schlichting waves due to the interaction between a small free-stream disturbance and a small localized variation of the surface geometry such as a hump or suction strip has been carried out using both finite difference and spectral methods. The nonlinear steady flow is of the viscous-inviscid interactive type while the unsteady disturbed flow is assumed to be governed by linearized disturbance equations. The numerical solutions illustrate the growth or decay of the TS waves generated by the interaction, depending on the value of a scaled Strouhal number.

On local boundary-layer receptivity to vortical disturbances in the free stream

2001 ◽  
Vol 449 ◽  
pp. 373-393 ◽  
Author(s):  
XUESONG WU
Keyword(s):  
Boundary Layer ◽  
Free Stream ◽  
Quantitative Agreement ◽  
Local Boundary ◽  
Upper Deck ◽  
Roughness Elements ◽  
Comprehensive Comparison ◽  
Tollmien Schlichting ◽  
Vortical Disturbance ◽  
Edge Layer

Prompted by the recent experiments of Dietz (1999) on boundary-layer receptivity due to a local roughness interacting with a vortical disturbance in the free stream, this paper undertakes to present a second-order asymptotic theory based on the tripledeck formulation. The asymptotic approach allows us to treat vortical perturbations with a fairly general vertical distribution, and confirms Dietz's conclusion that for the convecting periodic wake in his experiments, the receptivity is independent of its vertical structure and can be fully characterized by its slip velocity at the edge of the boundary layer. As in the case of distributed vortical receptivity, dominant interactions that generate Tollmien–Schlichting waves take place in the upper deck as well as in the so-called edge layer centred at the outer reach of the boundary layer. The initial amplitude of the excited Tollmien–Schlichting wave is determined to O(R−1/8) accuracy, where R is the global Reynolds number. An appropriate superposition formula is derived for the case of multiple roughness elements. A comprehensive comparison is made with Dietz's experimental data, and an excellent quantitative agreement has been found for the first time, thereby resolving some uncertainties about this receptivity mechanism.

Receptivity of boundary layers with distributed roughness to vortical and acoustic disturbances: a second-order asymptotic theory and comparison with experiments

2001 ◽  
Vol 431 ◽  
pp. 91-133 ◽  
Author(s):  
XUESONG WU
Keyword(s):  
Boundary Layer ◽  
Boundary Layers ◽  
Order Theory ◽  
Quantitative Agreement ◽  
Second Order ◽  
Acoustic Disturbances ◽  
First Order Theory ◽  
Theoretical Predictions ◽  
Tollmien Schlichting ◽  
Vortical Disturbance

This paper investigates the receptivity of boundary layers due to distributed roughness interacting with free-stream disturbances. Both acoustic and vortical perturbations are considered. An asymptotic approach based on the triple-deck formulation has been developed to determine the initial amplitude of the Tollmien–Schlichting wave to the O(R−1/8) accuracy, where R is the global Reynolds number. In the case of vortical disturbances, we show that the dominant contribution to the receptivity comes from the upper deck as well as from the so-called edge layer centred at the outer reach of the boundary layer. It is found that for certain forms of disturbances, the receptivity is independent of their vertical structure and can be fully characterized by their slip velocity at the edge of the boundary layer. A typical case is the vortical disturbance in the form of a convecting wake, for which the same conclusion as above has been reached by Dietz (1999) on the basis of measurements. Our theoretical predictions are compared with the experimental data of Dietz (1999), and a good quantitative agreement has been found. Such a comparison is the first to be made for distributed vortical receptivity. Further calculations indicate that the vortical receptivity in general is much stronger than was suggested previously. In the case of acoustic disturbances, it is found that our first-order theory is in good agreement with experiments as well as with previous theoretical results. But the second-order theory over-predicts, and the possible reasons for this are discussed.

Adjoint systems and their role in the receptivity problem for boundary layers

1995 ◽  
Vol 292 ◽  
pp. 183-204 ◽  
Author(s):  
D. C. Hill
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Acoustic Waves ◽  
Adjoint Problem ◽  
Neutral Stability ◽  
Free Shear Layer ◽  
Simple Method ◽  
Small Surface ◽  
Adjoint Systems ◽  
Tollmien Schlichting

The effectiveness with which various sources excite convective instabilities in a boundary layer is found by a simple method. Chosen field values of the adjoint to the Tollmien–Schlichting eigensolution, normalized appropriately, indicate the amplitude of the unstable disturbance which will result for direct time-harmonic forcing by sources of momentum, mass and vorticity, as well as by boundary motions. For the Blasius boundary layer, forcing in the vicinity of the critical layer induces the largest response. At this position, the response to forcing in the wall-normal direction is typically 5% of that resulting from streamwise forcing of the same magnitude. At the wall, normal motions elicit a much stronger response than streamwise motions. Forcing close to the lower branch of the neutral stability curve leads to the largest response. The adjoint field values are equivalent to the residues of Fourier-inversion integrals. This equivalence is discussed for two problems; the vibrating ribbon problem and excitation of an inviscid free shear layer by a vorticity source. The efficiency factor is calculated for the scattering of ‘acoustic’ waves into Tollmien–Schlichting waves in the presence of small surface roughness, at a finite Reynolds number, based on the Orr–Sommerfeld operator. This is achieved by using the solution of an inhomogeneous adjoint problem. The results are compared with the asymptotic solutions obtained from triple-deck theory, and agree with previous finite-Reynolds-number calculations.

Acoustic receptivity and evolution of two-dimensional and oblique disturbances in a Blasius boundary layer

2001 ◽  
Vol 432 ◽  
pp. 69-90 ◽  
Author(s):  
RUDOLPH A. KING ◽  
KENNETH S. BREUER
Keyword(s):  
Boundary Layer ◽  
Surface Roughness ◽  
Acoustic Wave ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Surface Waviness ◽  
S Wave ◽  
Boundary Layer Instability ◽  
Blasius Boundary Layer ◽  
Tollmien Schlichting

An experimental investigation was conducted to examine acoustic receptivity and subsequent boundary-layer instability evolution for a Blasius boundary layer formed on a flat plate in the presence of two-dimensional and oblique (three-dimensional) surface waviness. The effect of the non-localized surface roughness geometry and acoustic wave amplitude on the receptivity process was explored. The surface roughness had a well-defined wavenumber spectrum with fundamental wavenumber kw. A planar downstream-travelling acoustic wave was created to temporally excite the flow near the resonance frequency of an unstable eigenmode corresponding to kts = kw. The range of acoustic forcing levels, ε, and roughness heights, Δh, examined resulted in a linear dependence of receptivity coefficients; however, the larger values of the forcing combination εΔh resulted in subsequent nonlinear development of the Tollmien–Schlichting (T–S) wave. This study provides the first experimental evidence of a marked increase in the receptivity coefficient with increasing obliqueness of the surface waviness in excellent agreement with theory. Detuning of the two-dimensional and oblique disturbances was investigated by varying the streamwise wall-roughness wavenumber αw and measuring the T–S response. For the configuration where laminar-to-turbulent breakdown occurred, the breakdown process was found to be dominated by energy at the fundamental and harmonic frequencies, indicative of K-type breakdown.

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