Numerical investigation of zeros of some dispersion relations appearing in sound attenuation problems in a circular lined duct

• Main Authors: Loredana TANASIE, Agneta M. BALINT
• Format: Article
• Language: English
• Published: National Institute for Aerospace Research “Elie Carafoli” - INCAS 2012-12-01
• Series: INCAS Bulletin
• Subjects: aero acoustics; fluid dynamics; numerical investigation; sound attenuation problems
• Online Access: http://bulletin.incas.ro/files/balint_a__tanasie_l__v4_iss_4_full.pdf

In this paper the zeros of some dispersion relations apperaring in sound attenuation problems in circular lined ducts, carrying a gas flow, are investigated numerically. To find the values of frequencies for which the dispersion relations vanish is not easy at all. That is beacause these relations contain the solution of an initial value problem which depends on the unknown frequency and can not be found explicitly. In order to overcome this difficulty we consider approximate dispersion relations, obtained by replacing in the shear flow the solution of the initial value problem by its Taylor’s polynomial approximate. For numerical computations typical aeronautical examples are considered.