On the reflection and transmission of sound in a thick shear layer

2000 ◽  
Vol 424 ◽  
pp. 303-326 ◽  
Author(s):  
L. M. B. C. CAMPOS ◽  
M. H. KOBAYASHI
Keyword(s):  
Wave Equation ◽  
Mach Number ◽  
Shear Flow ◽  
Shear Layer ◽  
Acoustic Field ◽  
Free Stream ◽  
Finite Thickness ◽  
Vortex Sheet ◽  
Angle Of Incidence ◽  
Reflection And Transmission

The propagation of sound across a shear layer of finite thickness is studied using exact solutions of the acoustic wave equation for a shear flow with hyperbolic-tangent velocity profile. The wave equation has up to four regular singularities: two corresponding to the upper and lower free streams; one corresponding to a critical layer, where the Doppler-shifted frequency vanishes if the free streams are supersonic; and a fourth singularity which is always outside the physical region of interest. In the absence of a critical layer the matching of the two solutions, around the upper and lower free streams, specifies exactly the acoustic field across the shear layer. For example, for a sound wave incident from below (i.e. upward propagation in the lower free stream), the reflected wave (i.e. downward propagating in the lower free stream) and the transmitted wave (i.e. upward propagating in upper free stream) are specified by the continuity of acoustic pressure and vertical displacement. Thus the reflection and transmission coefficients, which are generally complex, i.e. involve amplitude and phase changes, are plotted versus angle of incidence for several values of free stream Mach number, and ratio of thickness of the shear layer to the wavelength; the vortex sheet is the particular case when the latter parameter is zero. The modulus and phase of the total acoustic field are also plotted versus the coordinate transverse to the shear flow, for several values of angle of incidence, Mach number and shear layer thickness. The analysis and plots in the present paper demonstrate significant differences between sound scattering by a shear layer of finite thickness, and the limiting case of the vortex sheet.

scholarly journals On the acoustics of an impedance liner with shear and cross flow

2014 ◽  
Vol 470 (2163) ◽  
pp. 20130732 ◽  
Author(s):  
L. M. B. C. Campos ◽  
C. Legendre ◽  
C. Sambuc
Keyword(s):  
Boundary Layer ◽  
Wave Equation ◽  
Shear Flow ◽  
Acoustic Field ◽  
Free Stream ◽  
Cross Flow ◽  
Angle Of Incidence ◽  
Third Order ◽  
Reflected Waves ◽  
Scattering Coefficients

The acoustic-vortical wave equation is derived describing the propagation of sound in (i) a unidirectional shear flow with a linear velocity profile upon which is superimposed (ii) a uniform cross flow; together with an impedance wall boundary condition representing the effect of a locally reacting acoustic liner in the presence of bias and shear flow. This leads to a third-order differential equation in the presence of cross flow, and in its absence simplifies to the Pridmore–Brown equation (second-order); also the singularity of the Pridmore–Brown equation for zero Doppler-shifted frequency is removed by the cross flow. Because the third-order wave equation has no singularities (except at the sonic condition), its general solution is a linear combination of three linearly independent MacLaurin series in powers of the distance from the wall. The acoustic field in the boundary layer is matched through the pressure and horizontal and vertical velocity components to the acoustic field in a uniform free stream consisting of incident and reflected waves. The scattering coefficients are plotted for several values of the five parameters of the problem, namely the angle of incidence, free stream and cross-flow Mach numbers, specific wall impedance and Helmholtz number using the boundary layer thickness.

Subsonic Flow Over Open Cavities: Part 1 — Analytical Models and Numerical Investigations

2016 ◽  
Author(s):  
Weidong Shao ◽  
Jun Li
Keyword(s):  
Boundary Layer ◽  
Mach Number ◽  
Shear Layer ◽  
Layer Thickness ◽  
Boundary Layer Thickness ◽  
Feedback Loop ◽  
Subsonic Flow ◽  
Free Stream ◽  
Open Cavities ◽  
Free Stream Mach Number

The aeroacoustical oscillation and acoustic field generated by subsonic flow grazing over open cavities has been investigated analytically and numerically. The tone generation mechanism is elucidated with an analytical model based on the coupling between shear layer instabilities and acoustic feedback loop. The near field turbulent flow is obtained using two-dimensional Large Eddy Simulation (LES). A special mesh is used to absorb propagating disturbances and prevent spurious numerical reflections. Comparisons with available experimental data demonstrate good agreement in both the frequency and amplitude of the aeroacoustical oscillation. The physical phenomenon of the noise generated by the feedback loop is discussed. The correlation analysis of primitive variables is also made to clarify the characteristics of wave propagation in space and time. The effects of free-stream Mach number and boundary layer thickness on pressure fluctuations within the cavity and the nature of the noise radiated to the far field are examined in detail. As free-stream Mach number increases velocity fluctuations and mass flux into the cavity increase, but the resonant Strouhal numbers slightly decrease. Both the resonant Strouhal numbers and sound pressure levels decrease with the increase of boundary layer thickness. Results indicate that the instability of the shear layer dominates both the frequency and amplitude of the aeroacoustical oscillation.

The structure of organized vortices in a free shear layer

1981 ◽  
Vol 102 ◽  
pp. 301-313 ◽  
Author(s):  
R. T. Pierrehumbert ◽  
S. E. Widnall
Keyword(s):  
Shear Layer ◽  
Finite Thickness ◽  
Major Axis ◽  
Vortex Sheet ◽  
Layer Growth ◽  
Approximate Theory ◽  
Free Shear Layer ◽  
Mathematical Basis ◽  
Energetic Properties ◽  
New Family

A new family of solutions to the steady Euler equations corresponding to spatially periodic states of a free shear layer is reported. This family bifurcates from a parallel shear layer of finite thickness and uniform vorticity, and extends continuously to a shear layer consisting of a row of concentrated pointlike vortices. The energetic properties of the family are considered, and it is concluded that a vortex in a row of uniform vortices produced by periodic roll-up of a vortex sheet must have a major axis of length approximately 50% or more of the distance between vortex centres; it is also concluded that vortex amalgamation events tend to reduce vortex size relative to spacing. The geometric and energetic properties of the solutions confirm the mathematical basis of the tearing mechanism of shear-layer growth first proposed in an approximate theory of Moore & Saffman (1975).

Subharmonic transition to turbulence in a flat-plate boundary layer at Mach number 4.5

1996 ◽  
Vol 317 ◽  
pp. 301-335 ◽  
Author(s):  
N. A. Adams ◽  
L. Kleiser
Keyword(s):  
Boundary Layer ◽  
Mach Number ◽  
Shear Layer ◽  
Flat Plate ◽  
Free Stream ◽  
Plate Boundary ◽  
Shear Layers ◽  
High Shear ◽  
Break Up ◽  
Flat Plate Boundary Layer

The subharmonic transition process of a flat-plate boundary layer at a free-stream Mach number of M∞ = 4.5 and a Reynolds number of 10000 based on free-stream velocity and initial displacement thickness is investigated by direct numerical simulation up to the beginning of turbulence. A second-mode instability superimposed with random noise of low amplitude is forced initially. The secondary subharmonic instability evolves from the noise in accordance with theory and leads to a staggered Λ-vortex pattern. Finite-amplitude Λ-vortices initiate the build-up of detached high-shear layers below and above the critical layer. The detached shear-layer generation and break-up are confined to the relative-subsonic part of the boundary layer. The breakdown to turbulence can be separated into two phases, the first being the break-up of the lower shear layer and the second being the break-up of the upper shear layer. Four levels of subsequent roll-up of the lower, Y-shaped shear layer have been observed, leading to new vortical structures which are unknown from transition at low Mach numbers. The upper shear layer behaviour is similar to that of the well-known high-shear layer in incompressible boundary-layer transition. It is concluded that, as in incompressible flow, turbulence is generated via a cascade of vortices and detached shear layers with successively smaller scales. The different phases of shear-layer break-up are also reflected in the evolution of averaged quantities. A strong decrease of the shape factor, as well as an increase of the skin friction coefficient, and a gradual loss of spanwise symmetry indicate the final breakdown to turbulence, where the mean velocity and temperature profiles approach those measured in fully turbulent flow.

Aspects of Shear Layer Unsteadiness in a Three-Dimensional Supersonic Wake

2005 ◽  
Vol 127 (6) ◽  
pp. 1085-1094 ◽  
Author(s):  
Alan L. Kastengren ◽  
J. Craig Dutton
Keyword(s):  
Shear Layer ◽  
Stream Flow ◽  
Free Stream ◽  
Angle Of Attack ◽  
Three Dimensional ◽  
Base Flow ◽  
Recirculation Region ◽  
Side View ◽  
Near Wake ◽  
Supersonic Wake

The near wake of a blunt-base cylinder at 10° angle-of-attack to a Mach 2.46 free-stream flow is visualized at several locations to study unsteady aspects of its structure. In both side-view and end-view images, the shear layer flapping grows monotonically as the shear layer develops, similar to the trends seen in a corresponding axisymmetric supersonic base flow. The interface convolution, a measure of the tortuousness of the shear layer, peaks for side-view and end-view images during recompression. The high convolution for a septum of fluid seen in the middle of the wake indicates that the septum actively entrains fluid from the recirculation region, which helps to explain the low base pressure for this wake compared to that for a corresponding axisymmetric wake.

Formation of Vortex Street in Laminar Boundary Layer

1980 ◽  
Vol 47 (2) ◽  
pp. 227-233 ◽  
Author(s):  
M. Kiya ◽  
M. Arie
Keyword(s):  
Boundary Layer ◽  
Shear Flow ◽  
Laminar Boundary Layer ◽  
Solid Wall ◽  
Vortex Sheet ◽  
Vortex Street ◽  
Bluff Bodies ◽  
Uniform Shear ◽  
Uniform Shear Flow ◽  
Vortex Patterns

Main features of the formation of vortex street from free shear layers emanating from two-dimensional bluff bodies placed in uniform shear flow which is a model of a laminar boundary layer along a solid wall. This problem is concerned with the mechanism governing transition induced by small bluff bodies suspended in a laminar boundary layer. Calculations show that the background vorticity of shear flow promotes the rolling up of the vortex sheet of the same sign whereas it decelerates that of the vortex sheet of the opposite sign. The steady configuration of the conventional Karman vortex street is not possible in shear flow. Theoretical vortex patterns are experimentally examined by a flow-visualization technique.

Standing acoustic waves in a low Mach number shear flow

AIAA Journal ◽  
1992 ◽  
Vol 30 (7) ◽  
pp. 1708-1715 ◽  
Author(s):  
Meng Wang ◽  
David R. Kassoy
Keyword(s):  
Mach Number ◽  
Shear Flow ◽  
Acoustic Waves ◽  
Low Mach Number

Effect of Mach number on the acoustic field of 2:1 elliptic-slot jet

2001 ◽  
Vol 105 (1043) ◽  
pp. 9-16 ◽  
Author(s):  
S. B. Verma ◽  
E. Rathakrishnan
Keyword(s):  
Mach Number ◽  
Fundamental Frequency ◽  
Acoustic Field ◽  
Major Axis ◽  
Shock Structure ◽  
Minor Axis ◽  
Noise Levels ◽  
Underexpanded Jets ◽  
Barrel Shock ◽  
Mach Numbers

Abstract The shock-structure and the related acoustic field of underexpanded jets undergoes significant changes as the Mach number Mj is increased. The present investigation is carried out to study the effect of Mach number on an underexpanded 2:1 elliptic-slot jet. Experimental data are presented for fully expanded Mach numbers ranging from 1.3 to 2.0. It is observed that the ‘cross-over’ point at the end of the first cell at low Mach numbers gets replaced by a normal shock at a highly underexpanded condition resulting in the formation of a ‘barrel’ shock along the minor-axis side with a ‘bulb’ shock formed along the major-axis side. The above change in shock structure is accompanied by a related change in the acoustic field. The amplitude of fundamental frequency along the minor-axis side grows with Mj but falls beyond Mj = 1.75. Along the major-axis side, however, the fundamental frequency does not exist at low Mach numbers. It appears at Mj = 1.75 but then falls at Mj = 2.0. The related azimuthal directivity of overall noise levels (OASPL) shows significant changes with Mj.

An Experimental Investigation of the Wake of an Axisymmetric Body with a Slanted Base

1983 ◽  
Vol 34 (1) ◽  
pp. 24-45 ◽  
Author(s):  
X.J. Xia ◽  
P.W. Bearman
Keyword(s):  
Drag Coefficient ◽  
Vortex Shedding ◽  
Free Stream ◽  
Sudden Change ◽  
Base Pressure ◽  
Wake Flow ◽  
Main Body ◽  
Angle Of Incidence ◽  
Slant Angle ◽  
Free Stream Turbulence

SummaryThe effect of base slant on the base pressure distribution, drag coefficient and vortex shedding characteristics of a model consisting of an axisymmetric main body with an ellipsoidal nose have been investigated for three fineness ratios; 3, 6 and 9. A sudden change in the drag coefficient and separated flow pattern is observed at a critical slant angle (for constant incidence) or at a critical angle of incidence (for a constant base slant angle). The tests confirm that the value of the maximum drag coefficient is extremely sensitive to angle of incidence. Measurements of the frequency of vortex shedding are presented and the structure of the wake is investigated using smoke visualization and hot-wire correlation measurements. The wake is found to be far less stable than that from a two-dimensional bluff body and the vortex structures are sometimes in-phase and sometimes out of phase across the wake. The effect of free-stream turbulence on this family of body shapes is observed to be different to that on three-dimensional blunt-faced bluff bodies. Free-stream turbulence is found to have a minimal effect on base pressure for slant angles giving a recirculating type near wake flow. When longitudinal vortices are present the addition of free-stream turbulence slightly reduces the magnitude of the peak suctions recorded on the base but has little effect on base drag.

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