scholarly journals On high-frequency sound generated by gust–aerofoil interaction in shear flow

2015 ◽  
Vol 766 ◽  
pp. 297-325 ◽  
Author(s):  
Lorna J. Ayton ◽  
N. Peake
Keyword(s):  
Shear Flow ◽  
Transition Region ◽  
High Frequency ◽  
Outer Region ◽  
Far Field ◽  
Radiated Power ◽  
Surface Transition ◽  
Trailing Edges ◽  
Parallel Shear Flow ◽  
Field Sound

AbstractA theoretical model is constructed to predict the far-field sound generated by high-frequency gust–aerofoil interaction in steady parallel shear flow, including the effects of aerofoil thickness. Our approach is to use asymptotic analysis of the Euler equations linearised about steady parallel shear flow, in the limits of high frequency and small, but non-zero, aerofoil thickness and Mach number. The analysis splits the flow into various regions around the aerofoil; local inner regions around the leading and the trailing edges where sound is generated and scattered; a surface transition region accounting for the curvature of the aerofoil; a wake transition region downstream of the aerofoil; and an outer region through which the sound propagates to the observer. Solutions are constructed in all regions, and matched using the principle of matched asymptotic expansions to yield the first two terms in the expansion of both the amplitude and the phase of the far-field pressure. Result are computed for the particular case of scattering of a gust by a symmetric Joukowski aerofoil placed in symmetric Gaussian parallel shear flow. The introduction of mean shear is shown to have a significant effect on the far-field directivity and on the total radiated power.

On high-frequency noise scattering by aerofoils in flow

2013 ◽  
Vol 734 ◽  
pp. 144-182 ◽  
Author(s):  
Lorna J. Ayton ◽  
N. Peake
Keyword(s):  
Transition Region ◽  
High Frequency ◽  
Angle Of Attack ◽  
Outer Region ◽  
Frequency Noise ◽  
Sound Waves ◽  
Incident Wavelength ◽  
Singular Perturbation Analysis ◽  
Trailing Edges ◽  
Valid Solution

AbstractA theoretical model is developed for the sound scattered when a sound wave is incident on a cambered aerofoil at non-zero angle of attack. The model is based on the linearization of the Euler equations about a steady subsonic flow, and is an adaptation of previous work which considered incident vortical disturbances. Only high-frequency sound waves are considered. The aerofoil thickness, camber and angle of attack are restricted such that the steady flow past the aerofoil is a small perturbation to a uniform flow. The singular perturbation analysis identifies asymptotic regions around the aerofoil; local ‘inner’ regions, which scale on the incident wavelength, at the leading and trailing edges of the aerofoil; Fresnel regions emanating from the leading and trailing edges of the aerofoil due to the coalescence of singularities and points of stationary phase; a wake transition region downstream of the aerofoil leading and trailing edge; and an outer region far from the aerofoil and wake. An acoustic boundary layer on the aerofoil surface and within the transition region accounts for the effects of curvature. The final result is a uniformly-valid solution for the far-field sound; the effects of angle of attack, camber and thickness are investigated.

Second-order recombination in a parallel shear flow

1989 ◽  
Vol 200 ◽  
pp. 389-407 ◽  
Author(s):  
Ronald Smith
Keyword(s):  
Shear Flow ◽  
Concentration Distribution ◽  
Second Order ◽  
Explicit Solutions ◽  
Far Field ◽  
First Order ◽  
Parallel Shear Flow

For a reactive solute, with weak second-order recombination, an investigation is made of the near-source behaviour (where concentrations are high), and of the far field (where the recombination has an accumulative effect). Despite the loss of material and increased spread due to recombination, the far-field concentration distribution is shown to be nearly Gaussian. This permits a simplified (Gaussian) treatment of the chemical nonlinearity. Explicit solutions are given for the total amount of solute, variance and kurtosis for solutes with no first-order reactions.

Sound Radiation From Shear Deformable Stiffened Laminated Plates With Multiple Compliant Layers

2012 ◽  
Vol 134 (5) ◽  
Author(s):  
Xiongtao Cao ◽  
Hongxing Hua
Keyword(s):  
High Frequency ◽  
Sound Pressure ◽  
Plate Theory ◽  
Sound Radiation ◽  
Laminated Plates ◽  
Far Field ◽  
Frequency Range ◽  
First Order ◽  
Shear Deformable ◽  
Field Sound

Sound radiation from shear deformable stiffened laminated plates with multiple compliant layers is theoretically studied. Equations of motion for the composite laminated plates are on the basis of the first-order shear deformation plate theory, and the transfer matrix method is used to describe sound transmission through compliant layers. The first and second sets of stiffeners interact with the plate through normal line forces. By using the Fourier transform and stationary phase method, the far-field sound pressure is obtained in terms of analytical expressions. Comparisons are made between the first-order shear deformation plate theory and the classical thin plate theory. Three principal conclusions are drawn in the study. (1) The transverse point force acting on the stiffeners yields lower far-field sound pressure in the middle and high frequency range. Specifically, the transverse point force exerting on the large stiffeners produces the lowest far-field sound pressure among three different reactive points at the plate, small stiffener and large stiffener. (2) The far-field sound pressure spectra are confined by an acoustic circle and remain unchanged. Lots of flexural waves in the structure cannot radiate sound into the far field. (3) The sound attenuation of stiffened plates with compliant layers is mainly caused by the sound isolation of compliant layers rather than vibrational reduction. Compliant layers can effectively reduce the radiated sound pressure in the medium and high frequency range.

Sound Radiation From Point Acoustic Sources With Shield of Large Prolate Spheroidal Baffles

2018 ◽  
Vol 140 (4) ◽  
Author(s):  
Xiongtao Cao ◽  
Mingsheng Wang ◽  
Lei Shi
Keyword(s):  
Coordinate System ◽  
High Frequency ◽  
Sound Pressure ◽  
Sound Radiation ◽  
Acoustic Power ◽  
Far Field ◽  
Frequency Range ◽  
Prolate Spheroidal ◽  
Sound Sources ◽  
Field Sound

Sound radiation from stationary and rotating point acoustic sources with shield of rigid prolate spheroidal baffles is explored in the prolate spheroidal coordinate system. The formulae of far-field sound pressure and acoustic power are derived and acoustic power spectral density (PSD) in terms of circumferential and azimuthal wavenumber is manifested from the low frequency range to high frequency range. Acoustic wave propagation features in the spherical coordinate system as a particular case of the prolate spheroidal coordinate system are presented. Rotating sound sources cause the frequency veering phenomenon and change the patterns of PSD. Some spheroidal harmonic waves with lower and higher wavenumber for the large prolate spheroids cannot contribute to far-field sound radiation in the high frequency range when sound sources are close to the axes of the spheroids. Sound pressure directivity and acoustic power of stationary point sound sources are also analyzed with the variation of source location.

Influence of incidence angle on sound generation by airfoils interacting with high-frequency gusts

1995 ◽  
Vol 292 ◽  
pp. 271-304 ◽  
Author(s):  
Matthew R. Myers ◽  
E. J. Kerschen
Keyword(s):  
High Frequency ◽  
Incidence Angle ◽  
Outer Region ◽  
Sound Field ◽  
Leading Edge ◽  
Edge Region ◽  
Sound Generation ◽  
Mean Flow ◽  
Flow Stagnation ◽  
Trailing Edges

A theoretical model is developed for the sound generated when a convected vortical or entropic gust encounters an airfoil at non-zero angle of attack. The theory is based on a linearization of the Euler equations about the steady subsonic flow past the airfoil. High-frequency gusts, whose wavelengths are short compared to the airfoil chord, but long compared to the displacement of the mean-flow stagnation point from the leading edge, are considered. The analysis utilizes singular-perturbation techniques and involves four asymptotic regions. Local regions, which scale on the gust wavelength, are present at the airfoil leading and trailing edges. Behind the airfoil a ‘transition’ region, which is similar to the transition zone between illuminated and shadow zones in optical problems, is present. In the outer region, far away from the airfoil edges and wake, the solution has a geometric-acoustics form. The primary sound generation is found to be concentrated in the local leading-edge region. The trailing edge plays a secondary role as a scatterer of the sound generated in the leading-edge region. Parametric calculations are presented which illustrate that moderate levels of airfoil steady loading can significantly affect the sound field produced by airfoil–gust interactions.

scholarly journals Structural and Acoustic Responses of a Submerged Stiffened Conical Shell

2014 ◽  
Vol 2014 ◽  
pp. 1-14 ◽  
Author(s):  
Meixia Chen ◽  
Cong Zhang ◽  
Xiangfan Tao ◽  
Naiqi Deng
Keyword(s):  
Conical Shell ◽  
Element Model ◽  
Analytical Models ◽  
Superposition Method ◽  
Far Field ◽  
Fluid Loading ◽  
Low Frequencies ◽  
Structural Responses ◽  
The Individual ◽  
Field Sound

This paper studies the vibrational behavior and far-field sound radiation of a submerged stiffened conical shell at low frequencies. The solution for the dynamic response of the conical shell is presented in the form of a power series. A smeared approach is used to model the ring stiffeners. Fluid loading is taken into account by dividing the conical shell into narrow strips which are considered to be local cylindrical shells. The far-field sound pressure is solved by the Element Radiation Superposition Method. Excitations in two directions are considered to simulate the loading on the surface of the conical shell. These excitations are applied along the generator and normal to the surface of the conical shell. The contributions from the individual circumferential modes on the structural responses of the conical shell are studied. The effects of the external fluid loading and stiffeners are discussed. The results from the analytical models are validated by numerical results from a fully coupled finite element/boundary element model.

ANALYSIS OF A HETEROGENEOUS DOMAIN DECOMPOSITION FOR COMPRESSIBLE VISCOUS FLOW

2001 ◽  
Vol 11 (04) ◽  
pp. 565-599 ◽  
Author(s):  
CRISTIAN A. COCLICI ◽  
WOLFGANG L. WENDLAND
Keyword(s):  
Domain Decomposition ◽  
Stokes Equations ◽  
Domain Decomposition Method ◽  
Near Field ◽  
Outer Region ◽  
Navier Stokes ◽  
Far Field ◽  
Computational Domain ◽  
Linearized Euler Equations ◽  
Naca0012 Airfoil

We analyze a nonoverlapping domain decomposition method for the treatment of two-dimensional compressible viscous flows around airfoils. Since at some distance to the given profile the inertial forces are strongly dominant, there the viscosity effects are neglected and the flow is assumed to be inviscid. Accordingly, we consider a decomposition of the original flow field into a bounded computational domain (near field) and a complementary outer region (far field). The compressible Navier–Stokes equations are used close to the profile and are coupled with the linearized Euler equations in the far field by appropriate transmission conditions, according to the physical properties and the mathematical type of the corresponding partial differential equations. We present some results of flow around the NACA0012 airfoil and develop an a posteriori analysis of the approximate solution, showing that conservation of mass, momentum and energy are asymptotically attained with the linear model in the far field.

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