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

[+] Author and Article Information
B. Manoj Kumar, R. I. Sujith

Department of Aerospace Engineering, Indian Institute of Technology, Madras, India 600036

J. Vib. Acoust 120(4), 965-969 (Oct 01, 1998) (5 pages) doi:10.1115/1.2893927 History: Received June 01, 1996; Online February 26, 2008


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 of Bessel 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.

Copyright © 1998 by The American Society of Mechanical Engineers
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