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.

R. I. Sujith

Department of Aerospace Engineering

B. Balanaga Karthik

R. Krishna Mohanraj

acoustics

article

mathematical analysis

priority journal

SOUND TRANSMISSION

temperature dependence

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IIT Madras

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

Journal of the Acoustical Society of America

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.

Journal of Vibration and Acoustics, Transactions of the 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

This paper describes a theoretical investigation of the possibility of improving the performance of packed bed dryers using acoustic oscillations. It was motivated by the increasing interest in the use of acoustic oscillations to improve the performance of energy-intensive, industrial processes. Sound propagation in a packed bed was modelled as propagation through a porous medium. The effect of acoustic oscillations on the drying rate was then investigated by numerically integrating the heat and mass transfer equations. The model used quasi-steady correlations for heat and mass transfer. The results show that threshold values for void fractions and sound pressure levels exist, above which significant increase in drying rate can be obtained. The increase in mass transfer decreases with effective particle diameter.

Canadian Journal of Chemical Engineering

A theoretical investigation of enhancement of mass transfer from a packed bed using acoustic oscillations

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.

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

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.

Journal	Journal of the Acoustical Society of America
ISSN	00014966
Open Access	No