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.

R. I. Sujith

Department of Aerospace Engineering

acoustics

analytic method

article

priority journal

SOUND TRANSMISSION

Temperature

IIT Madras is a public technical and research university located in Chennai, Tamil Nadu. Founded in 1959, it is recognised as an Institute of National Importance.

IIT Madras has been ranked as the top engineering institute in India for four years in a row by the National Institutional Ranking Framework of the MHRD

It currently offers undergraduate, postgraduate and research degrees across 16 disciplines in Engineering, Sciences, Humanities and Management. About 596 faculty belonging to science and engineering departments and centres of the Institute are engaged in teaching, research and industrial consultancy.

IIT Madras

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

Journal of the Acoustical Society of America

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.

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

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.

Journal of Vibration and Acoustics, Transactions of the ASME

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

Journal of Sound and Vibration

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

Theoretical study of flow turning losses in the presence of mean temperature gradients

The Journal of the Acoustical Society of America

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

The transfer matrix of a uniform duct with a linear temperature gradient

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