Archives of Acoustics, 44, 2, pp. 239–249, 2019
10.24425/aoa.2019.128487

Sound Wave Radiation from Partially Lined Duct

Burhan TIRYAKIOGLU
Marmara University
Turkey

Ahmet DEMIR
Karabuk University
Turkey

The radiation of sound waves from partially lined duct is treated by using the mode-matching method in conjunction with the Wiener-Hopf technique. The solution is obtained by modification of the Wiener-Hopf technique and involves an infinite series of unknowns which are determined from an infinite system of linear algebraic equations. Numerical solution of this system is obtained for various values of the problem parameters, whereby the effects of these parameters on the sound diffraction are studied. A perfect agreement is observed when the results of radiated field are compared numerically with a similar work existing in the literature.
Keywords: Wiener-Hopf; Fourier transform; duct; saddle point
Full Text: PDF

References

Abramowitz M., Stegun I. (1964), Handbook of mathematical functions, Dover, New York.

Büyükaksoy A., Demir A. (2006), Radiation of sound from a semi-infinite rigid duct inserted axially into a larger infinite tube with wall impedance discontinuity, Journal of Applied Mathematics and Mechanics – ZAMM, 86, 563–571.

Büyükaksoy A., Demir A., Hacivelioglu F. (2008), Propagation of waves in a bifurcated cylindrical waveguide with wall impedance discontinuity, Progress in Electromagnetics Research B, 6, 295–306.

Büyükaksoy A., Polat B. (1997), Scalar wave diffraction by a rigid cylindrical rod of finite length with impedance ends, Journal of Applied Mathematics and Mechanics – ZAMM, 77, 11, 839–848.

Büyükaksoy A., Polat B. (1998), Diffraction of acoustic waves by a semi-infinite cylindrical impedance pipe of certain wall thickness, Journal of Engineering Mathematics, 33, 4, 333–352.

Demir A., B¨uy¨ukaksoy A. (2003), Radiation of plane sound waves by a rigid circular cylindrical pipe with a partial internal impedance loading, Acta Acustica United with Acustica, 89, 4, 578–585.

Demir A., Rienstra S. (2010), Sound radiation from a lined exhaust duct with lined afterbody, 16th AIAA/CEAS Aeroacoustics Conference, pp. 1–18, Stockholm, Sweden.

Levine H., Schwinger J. (1948), On the radiation of sound from an unflanged circular pipe, Physical Review, 73, 4, 383–406.

Noble B. (1958), Methods based on the Wiener-Hopf techniques, Pergamon Press, London.

Rawlins A.D. (1978), Radiation of sound from an unflanged rigid cylindrical duct with an acoustically absorbing internal surface, Proceedings of the Royal Society of London A, 361, 1704, 65–91.

Rienstra S., Peake N. (2005), Modal scattering at an impedance transition in a lined flow duct, 11th AIAA/CEAS Aeroacoustics Conference, pp. 1–19, Monterey, CA, USA.

Snakowska A. (1992), The acoustic far field of an arbitrary Bessel mode radiating from a semi-infinite unflanged cylindrical wave-guide, Acta Acustica United with Acustica, 77, 2, 53–62.

Snakowska A. (2008), Diffraction of sound waves at the opening of a soft cylindrical duct, European Physical Journal Special Topics, 154, 1, 201–206.

Snakowska A., Idczak H. (2006), The saddle point method applied to selected problems of acoustics, Archives of Acoustics, 31, 1, 57–76.

Snakowska A., Jurkiewicz J., Gorazd L. (2017), A hybrid method for determination of the acoustic impedance of an unflanged cylindrical duct for multimode wave, Journal of Sound and Vibration, 396, 325–339.

Tiryakioglu B., Demir A. (2016), Diffraction of acoustic waves by a semi-infinite pipe with finite impedance discontinuity, 4th International Symposium on Innovative Technologies in Engineering and Science, pp. 150–159, Antalya, Turkey.

Turetken B., Büyükaksoy A., Demir A. (2003), Radiation of sound waves from a rigid stepped cylindrical waveguide, Journal of Engineering Mathematics, 46, 1, 33–54.

Weinstein L.A. (1969), The theory of diffraction and the factorization method, Golem Press, Boulder, Colorado.

Zorumski W.E. (1973), Generalised radiation impedances and reflection coefficients of circular and annular ducts, Journal of Acoustical Society of America, 54, 6, 1667–1673.




DOI: 10.24425/aoa.2019.128487

Copyright © Polish Academy of Sciences & Institute of Fundamental Technological Research (IPPT PAN)