The purpose of this paper is to present closed form expressions for sound propagation in ducts with polynomial mean temperature profiles. It is shown that using appropriate transformations, the one-dimensional wave equation for ducts with an axial mean temperature gradient can be reduced to a standard differential equation whose form depends upon the specific mean temperature profile in the duct. The solutions are obtained in terms ofBessel and Neumann functions. The analysis neglects the effects of mean flow and therefore the solutions obtained are valid only for mean mach numbers that are less than 0.1. The developed solution is used to investigate the sound propagation in a quarter wave tube with an axial mean temperature gradient. The expressions for the four pole parameters are also presented. © 1998 by ASME.

R. I. Sujith

Department of Aerospace Engineering

Combustors

Ducts

Temperature distribution

Temperature profiles

ACOUSTIC FIELD MEASUREMENT

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IIT Madras

Exact Solution for One-Dimensional Acoustic Fields in Ducts With Polynomial Mean Temperature Profiles

Journal of Vibration and Acoustics, Transactions of the ASME

Exact solutions for one-dimensional, transient acoustic wave propagation in curvilinear geometries with mean temperature variations are presented in this paper. These solutions are obtained by using a transformation of the spatial and acoustic variables in a manner suggested by the WKB approximation. The analysis is performed for spherical and cylindrical co-ordinate systems. Temperature profiles admitting exact traveling wave type solutions are derived. Although these solutions resemble the approximate, “high frequency,” WKB form of solution of the wave equation, they have the interesting property that they are exact, regardless of the scale of the acoustic disturbance relative to that of the inhomogeneity. Calculations showing the propagation of waves in cylindrical and spherical geometries are presented. © 2003 by ASME.

Propagation of sound in inhomogeneous media: Exact, transient solutions in curvilinear geometries

This paper presents a family of exact solutions for quasi-one-dimensional, transient acoustic wave propagation in ducts with mean temperature and area variations in the absence of mean flow. These solutions are obtained using a transformation of the spatial and acoustic variables in a manner suggested by the WKB approximation. Exact travelling wave-type solutions are obtained for a class of temperature and area profiles. These solutions differ from the classical travelling wave solution, however, in that the acoustic pressure and velocity are not algebraically related by the local value of the acoustic impedance, ρ̄(x)c̄(x). Although these solutions resemble the approximate, "high frequency", WKB form of solution of the wave equation, they have the interesting property that they are exact, regardless of the scale of the acoustic disturbance relative to that of the inhomogeneity. © 2001 Academic Press.

Journal of Sound and Vibration

A family of exact transient solutions for acoustic wave propagation in inhomogeneous, non-uniform area ducts

An exact solution for one-dimensional sound propagation in ducts in the presence of axial mean temperature gradient and particulate damping is presented in this paper. The acoustic wave equation is derived starting from the one-dimensional momentum and energy equation. The application of appropriate transformations leads to an analytically solvable Whittaker's differential equation for the case of a linear mean temperature gradient and Bessel's differential equation for the case of an exponential mean temperature gradient. The derived analytical solutions are used to investigate the dependence of the acoustic field in a duct on temperature gradient and particulate damping.

Journal of the Acoustical Society of America

Exact solution for sound propagation in ducts with an axial mean temperature gradient and particulate damping

The purpose of this Letter is to present an exact analytical solution for sound propagation in ducts with a quadratic mean temperature profile. Using appropriate transformations, the one-dimensional wave equation for ducts with an axial mean temperature gradient was reduced to the hypergeometric differential equation, whose solution can be expressed in terms of hypergeometric functions. The analysis neglects the effects of mean flow and is therefore valid only for small mean Mach numbers.

Exact solution for one-dimensional acoustic fields in ducts with a quadratic mean temperature profile

An exact solution for one-dimensional acoustic fields in ducts with an axial temperature gradient

32nd Aerospace Sciences Meeting and Exhibit

Exact solution for one-dimensional acoustic fields in ducts with axial temperature gradient

The Journal of the Acoustical Society of America

Thermoacoustics of traveling waves: Theoretical analysis for an inviscid ideal gas

Combustion and Flame

Oscillatory velocity response of premixed flat flames stabilized in axial acoustic fields

Exact solution for one-dimensional acoustic fields in ducts with polynomial mean temperature profiles

Journal	Journal of Vibration and Acoustics, Transactions of the ASME
ISSN	10489002
Open Access	No